Search

In this paper, by using the Nehari manifold approach in combination with periodic approximations, we obtain the sufficient conditions on the existence of the nontrivial ground state solutions of the periodic discrete coupled nonlinear Schrodinger equations. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, a novel 3D nonlinear system with chaotic behavior is considered. Our proposed system is a generalized Lorenz-like system, with no reflections about coordinates axes. Although the considered system depends on seven real parameters, its stability is completely analyzed. Also, the presence of Hopf bifurcation is pointed out. Copyright © 2014 John Wiley & Sons, Ltd.

This paper is concerned with the nonlinear Dirac equations Under suitable assumptions on the nonlinearity, we establish the existence of infinitely many large energy solutions by the generalized variant fountain theorem developed recently by Batkam and Colin. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we will obtain that there exists a maximizer for the non-endpoint Strichartz inequalities for the fourth-order Schrodinger equation with initial data in the L2(Rd) space in all dimensions, and then we obtain a maximizer also for the non-endpoint Sobolev–Strichartz inequality for the fourth-order Schrodinger equation with initial data in the homogeneous Sobolev space. Our analysis derived from the linear profile decomposition. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, the analytical approximate traveling wave solutions of Whitham–Broer–Kaup (WBK) equations, which contain blow-up solutions and periodic solutions, have been obtained by using the coupled fractional reduced differential transform method. By using this method, the solutions were calculated in the form of a generalized Taylor series with easily computable components. The convergence of the method as applied to the WBK equations is illustrated numerically as well as analytically. By using the present method, we can solve many linear and nonlinear coupled fractional differential equations. The results justify that the proposed method is also very efficient, effective and simple for obtaining approximate solutions of fractional coupled modified Boussinesq and fractional approximate long wave equations. Numerical solutions are presented graphically to show the reliability and efficiency of the method. Moreover, the results are compared with those obtained by the Adomian decomposition method (ADM) and variational iteration method (VIM), revealing that the present method is superior to others. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we consider an inverse source problem of identification of F(t) function in the linear parabolic equation ut = uxx + F(t) and u0(x) function as the initial condition from the measured final data and local boundary data. Based on the optimal control framework by Green's function, we construct Frechet derivative of Tikhonov functional. The stability of the minimizer is established from the necessary condition. The CG algorithm based on the Frechet derivative is applied to the inverse problem, and results are presented for a test example. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, a mathematical model for HIV-1 infection with antibody, cytotoxic T-lymphocyte immune responses and Beddington–DeAngelis functional response is investigated. The stability of the infection-free and infected steady states is investigated. The basic reproduction number R0 is identified for the proposed system. If R0 1 in the absence of immune response delay. We use Nyquist criterion to estimate the length of the delay for which stability continues to hold. Also the existence of the Hopf bifurcation is investigated by using immune response delay as a bifurcation parameter. Numerical simulations are presented to justify the analytical results. Copyright © 2014 John Wiley & Sons, Ltd.

We study the ultra-relativistic Euler equations for an ideal gas, which is a system of nonlinear hyperbolic conservation laws. We first analyze the single shocks and rarefaction waves and solve the Riemann problem in a constructive way. Especially, we develop an own parametrization for single shocks, which will be used to derive a new explicit shock interaction formula. This shock interaction formula plays an important role in the study of the ultra-relativistic Euler equations. One application will be presented in this paper, namely, the construction of explicit solutions including shock fronts, which gives an interesting example for the non-backward uniqueness of our hyperbolic system. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we propose a new class of functions called pseudo -asymptotically ω-periodic function in the Stepanov sense and explore its properties in Banach spaces including composition results. Furthermore, the existence and uniqueness of the pseudo -asymptotically ω-periodic mild solutions to Volterra integro-differential equations is investigated. Applications to integral equations arising in the study of heat conduction in materials with memory are shown. Copyright © 2014 John Wiley & Sons, Ltd.

We study in this paper the Dirichlet boundary value problem of second-order differential system in the form where u ∈ Rn,A,B ∈ Rn,M ∈ Rn × n is a symmetric matrix, F : [0,1] × Rn Rn such a system comes from a model describing the vibration of a multi-storey building. By using the saddle point theorem, we prove an existence theorem for the solutions to the given system. Copyright © 2014 John Wiley & Sons, Ltd.

A diffusive predator–prey model with predator saturation and competition response subject to homogeneous Neumann boundary conditions is considered in this paper. We find that the spatially homogeneous and non-homogeneous periodic solutions through all parameters of the system are spatially homogeneous. To verify our theoretical results, some numerical simulations are also carried out. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we study a virus dynamics model with logistic mitosis, cure rate, and intracellular delay. By means of construction of a suitable Lyapunov functionals, obtained by linear combinations of Volterra—type functions, composite quadratic functions and Volterra—type functionals, we provide the global stability for this model. If R0, the basic reproductive number, satisfies R0 ≤ 1, then the infection-free equilibrium state is globally asymptotically stable. Our system is persistent if R0 > 1. On the other hand, if R0 > 1, then infection-free equilibrium becomes unstable and a unique infected equilibrium exists. The local stability analysis is carried out for the infected equilibrium, and it is shown that, if the parameters satisfy a condition, the infected equilibrium can be unstable and a Hopf bifurcation can occur. We also have that if R0 > 1, then the infected equilibrium state is globally asymptotically stable if a sufficient condition is satisfied. We illustrate our findings with some numerical simulations. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, the Schrodinger operator where the potential q(x) is single-well with transition point is considered. Suppose {λn}n ≥ 1 is the set of eigenvalues for the previous Schrodinger operator and the potential q(x) possesses an additional condition, we show that the first two eigenvalues λ2 and λ1 satisfy Equality holds if and only if q(x) is a constant. Copyright © 2014 John Wiley & Sons, Ltd.

This paper is concerned with a class of fourth-order nonlinear difference equations. By using the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of solutions for Dirichlet boundary value problems and give some new results. Our results successfully complement the existing ones. Copyright (c) 2014 John Wiley & Sons, Ltd.

In this paper, the global stability of a virus dynamics model with intracellular delay, Crowley–Martin functional response of the infection rate, and CTL immune response is studied. By constructing suitable Lyapunov functions and using LaSalles invariance principle, the global dynamics is established; it is proved that if the basic reproductive number, R0, is less than or equal to one, the infection-free equilibrium is globally asymptotically stable; if R0 is more than one, and if immune response reproductive number, R0, is less than one, the immune-free equilibrium is globally asymptotically stable, and if R0 is more than one, the endemic equilibrium is globally asymptotically stable. Copyright © 2014 John Wiley & Sons, Ltd.

In many cases, multiphase flows are simulated on the basis of the incompressible Navier–Stokes equations. This assumption is valid as long as the density changes in the gas phase can be neglected. Yet, for certain technical applications such as fuel injection, this is no longer the case, and at least the gaseous phase has to be treated as a compressible fluid. In this paper, we consider the coupling of a compressible flow region to an incompressible one based on a splitting of the pressure into a thermodynamic and a hydrodynamic part. The compressible Euler equations are then connected to the Mach number zero limit equations in the other region. These limit equations can be solved analytically in one space dimension that allows to couple them to the solution of a half-Riemann problem on the compressible side with the help of velocity and pressure jump conditions across the interface. At the interface location, the flux terms for the compressible flow solver are provided by the coupling algorithms. The coupling is demonstrated in a one-dimensional framework by use of a discontinuous Galerkin scheme for compressible two-phase flow with a sharp interface tracking via a ghost-fluid type method. The coupling schemes are applied to two generic test cases. The computational results are compared with those obtained with the fully compressible two-phase flow solver, where the Mach number zero limit is approached by a weakly compressible fluid. For all cases, we obtain a very good agreement between the coupling approaches and the fully compressible solver. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we establish the local existence of strong solutions to an Oldroyd-B model for the incompressible viscoelastic fluids in a bounded domain , via the incompressible limit. The main idea is to derive the uniform estimates with respect to the Mach number for the linearized system of compressible Oldroyd equations. Copyright © 2014 John Wiley & Sons, Ltd.

This paper is concerned with the generalized nonlinear Schrodinger equation with parabolic law and dual-power law. Abundant explicit and exact solutions of the generalized nonlinear Schrodinger equation with parabolic law and dual-power law are derived uniformly by using the first integral method. These exact solutions are include that of extended hyperbolic function solutions, periodic wave solutions of triangle functions type, exponential form solution, and complex hyperbolic trigonometric function solutions and so on. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial DEs. Copyright © 2014 John Wiley & Sons, Ltd.

The electromagnetic interior transmission problem is a boundary value problem, which is neither elliptic nor self-adjoint. The associated transmission eigenvalue problem has important applications in the inverse electromagnetic scattering theory for inhomogeneous media. In this paper, we show that, in general, there do not exist purely imaginary electromagnetic transmission eigenvalues. For constant index of refraction, we prove that it is uniquely determined by the smallest (real) transmission eigenvalue. Finally, we show that complex transmission eigenvalues must lie in a certain region in the complex plane. The result is verified by examples. Copyright © 2014 John Wiley & Sons, Ltd.

This paper proposes two modified susceptible-infected-recovered (SIRS) models on homogenous and heterogeneous networks, respectively. In the study of the homogenous network model, Lyapunov functions are used to study the globally asymptotically stable of the equilibria of the model. It is proved that if the basic reproduction number of the model is less than one, then the disease-free equilibrium is globally asymptotically stable, otherwise, the endemic equilibrium is globally asymptotically stable. In the study of the heterogeneous network model, the existences of the disease-free equilibrium and epidemic equilibrium of the model are discussed. A threshold value is given. It is proved that if the threshold value of the model is less than one, then the disease-free equilibrium is globally asymptotically stable. The simulation examples on the two SIRS models are given. Copyright © 2013 John Wiley & Sons, Ltd.

This paper presents an efficient numerical method for finding solutions of the nonlinear Fredholm integral equations system of second kind based on Bernstein polynomials basis. The numerical results obtained by the present method have been compared with those obtained by B-spline wavelet method. This proposed method reduces the system of integral equations to a system of algebraic equations that can be solved easily any of the usual numerical methods. Numerical examples are presented to illustrate the accuracy of the method. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we consider an almost periodic discrete Lotka–Volterra mutualism model with delays. We first obtain the permanence and global attractivity of the system. By means of an almost periodic functional hull theory and constructing a suitable Lyapunov function, sufficient conditions are obtained for the existence of a unique strictly positive almost periodic solution, which is globally attractive. An example together with numerical simulation indicates the feasibility of the main result. Copyright © 2013 John Wiley & Sons, Ltd.

This paper discusses templates for designing efficient and robust multigrid (MG) methods. All MG mechanisms are described by means of matrix functions (block symbols), which capture the properties of the full matrices. We propose a new strategy for deriving the block symbol by means of sparse matrices and of its representation in terms of the usual tensor product. Emphasis is laid on the indefinite Helmholtz equation, which is of great practical interest in real-life applications. We take advantage of previously known patterns (the subblock smoother as preconditioner and the full projection as grid transfer operator) for designing MG methods that work as direct solvers. The corresponding numerical results are presented and the superiority of the combined use of a subblock smoother and a full projection is demonstrated. The condition number and positive definiteness of the subblock smoother especially for Helmholtz-like problems are analyzed, and the corresponding requirements and bounds are given. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we consider a nonlinear sublinear Schrodinger equation at resonance in . By using bounded domain approximation technique, we prove that the problem has infinitely many solutions. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we investigate a class of singular third-order differential equations with variable coefficients. By application of Green's functions and Schauder's fixed point theorem, sufficient conditions for the existence of positive periodic solutions are established. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we construct and study a new generalized convolution (f * g)(x) of functions f,g for the Hartley (H1,H2) and the Fourier sine (Fs) integral transforms. We will show that these generalized convolutions satisfy the following factorization equalities: We prove the existence of this generalized convolution on different function spaces, such as . As examples, applications to solve a type of integral equations and a type of systems of integral equations are presented. Copyright © 2013 John Wiley & Sons, Ltd.

The general notion of 'strong' stability for internal autonomous system descriptions has been recently introduced for continuous and discrete-time systems. This is a stronger notion of stability compared with alternative definitions (asymptotic, Lyapunov), which prohibits systems described by natural coordinates to have overshooting responses, for arbitrary initial conditions in state space. The paper reviews three refined notions of strong stability, along with the necessary and sufficient conditions corresponding to each notion. Using the Cayley transformation, it is shown that the notions in the two domains are essentially equivalent and that the strong stability conditions can be transformed from one domain to the other in a straightforward way. © 2013 John Wiley & Sons, Ltd.

In this paper, we show the existence and uniqueness of the mild solution for a class of time-dependent stochastic evolution equations with finite delay driven by a standard cylindrical Wiener process and an independent cylindrical fractional Brownian motion with Hurst parameter H ∈ (1 / 2,1). An example is provided to illustrate the theory. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we consider the Petrov–Galerkin spectral method for fourth-order elliptic problems on rectangular domains subject to non-homogeneous Dirichlet boundary conditions. We derive some sharp results on the orthogonal approximations in one and two dimensions, which play important roles in numerical solutions of higher-order problems. By applying these results to a fourth-order problem, we establish the H2-error and L2-error bounds of the Petrov–Galerkin spectral method. Numerical experiments are provided to illustrate the high accuracy of the proposed method and coincide well with the theoretical analysis. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we consider an eco-epidemiological model with Holling type III functional response and a time delay representing the gestation period of the predator. In the model, it is assumed that the predator population suffers a transmissible disease. By means of Lyapunov functionals and Laselle’s invariance principle, sufficient conditions are obtained for the global stability of the endemic coexistence of the system.

In this paper, a stage-structured SI epidemic model with time delay and nonlinear incidence rate is investigated. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium, and the existence of Hopf bifurcations are established. By comparison arguments, it is proved that if the basic reproduction number is less than unity, the disease-free equilibrium is globally asymptotically stable. If the basic reproduction number is greater than unity, by means of an iteration technique, sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we consider the existence of solutions for second-order nonlinear damped impulsive differential equations with Dirichlet boundary condition. By critical point theory, we obtain some existence theorems of solutions for the nonlinear problem. We extend and improve some recent results. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we give error estimates for quadrature rules with maximal trigonometric degree of exactness with respect to an even weight function on ( − π,π) for integrand analytic in a certain domain of complex plane. Copyright © 2013 John Wiley & Sons, Ltd.

Let l(alpha) be the fractional integral on the Euclidean space R-n, where alpha is an element of (0, n). Assume that Phi and Psi are two Orlicz functions satisfying i(Phi), i(Psi) is an element of (0, 1], and Psi(-1)(t) = Phi(-1)(t)t(-alpha/n) n for all t is an element of (0, infinity), where i(Phi) and i(Psi) are, respectively, the critical lower type indices of Phi and Psi, and Phi(-1) and Psi(-1) their inverses. In this paper, the authors prove that I-alpha is bounded from the weighted Orlicz-Hardy space H-w(Phi)(R-n) to the weighted Orlicz-Hardy space H-w(Psi)(R-n), whenever there exist 1 < p(1) < q(1) < infinity, satisfying 1/p(1) - 1/q(1) = alpha/n, such that w(1/q1) belongs to the A(p1,q1) (R-n) weight. To this end, the authors first establish the atomic and the molecular characterizations of theseweightedOrlicz-Hardy spaces, which are defined via the nontangential grand maximal function. Thus, as a byproduct, the authors establish the nontangential grand maximal function and molecular characterizations of the weighted atomic Orlicz-Hardy space introduced by Harboure, Salinas, and Viviani. Copyright (C) 2013 JohnWiley & Sons, Ltd.

In this paper, we state and prove a new formula expressing explicitly the integratives of Bernstein polynomials (or B-polynomials) of any degree and for any fractional-order in terms of B-polynomials themselves. We derive the transformation matrices that map the Bernstein and Legendre forms of a degree-n polynomial on [0,1] into each other. By using their transformation matrices, we derive the operational matrices of integration and product of the Bernstein polynomials. These matrices together with the Tau method are then utilized to reduce the solution of this problem to the solution of a system of algebraic equations. The method is applied to solve linear and nonlinear fractional differential equations. Copyright © 2013 John Wiley & Sons, Ltd.

Klein–Gordon equation models many phenomena in both physics and applied mathematics. In this paper, a coupled method of Laplace transform and Legendre wavelets, named (LLWM), is presented for the approximate solutions of nonlinear Klein–Gordon equations. By employing Laplace operator and Legendre wavelets operational matrices, the Klein–Gordon equation is converted into an algebraic system. Hence, the unknown Legendre wavelets coefficients are calculated in the form of series whose components are computed by applying a recursive relation. Block pulse functions are used to calculate the Legendre wavelets coefficient vectors of nonlinear terms. The convergence analysis of the LLWM is discussed. The results show that LLWM is very effective and easy to implement. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, a virus dynamics model with intracellular delay and Crowley–Martin functional response is discussed. By constructing suitable Lyapunov functions and using LaSalles invariance principle for delay differential equations, we established the global stability of uninfected equilibrium and infected equilibrium; it is proved that if the basic reproductive number is less than or equal to one, the uninfected equilibrium is globally asymptotically stable; if the basic reproductive number is more than one, the infected equilibrium is globally asymptotically stable. We also discuss the effects of intracellular delay on global dynamical properties by comparing the results with the stability conditions for the model without delay. Copyright © 2013 John Wiley & Sons, Ltd.

In the present paper, we consider the dissipative coupled fractional Schrodinger equations. The global well-posedness by the contraction mapping principle is obtained. We study the long time behavior of solutions for the Cauchy problem. We prove the existence of global attractor. Copyright © 2013 John Wiley & Sons, Ltd.

This paper is concerned with the numerical solution of delay integro-differential equations. The main purpose of this work is to provide a new numerical approach based on the use of continuous collocation Taylor polynomials for the numerical solution of delay integro-differential equations. It is shown that this method is convergent. Numerical illustrations confirm our theoretical analysis. Copyright © 2013 John Wiley & Sons, Ltd.

This paper deals with the following doubly degenerate parabolic system with null Dirichlet boundary conditions in a smooth bounded domain Ω ⊂ RN, where m, n ≥ 1, p, q ≥ 2, r1, r2, s1, s2 ≥ 1, α, β

This paper is concerned with the existence of traveling waves to a predator–prey model with a spatiotemporal delay. By analyzing the corresponding characteristic equations, the local stability of a positive steady state and each of boundary steady states are established, and the existence of Hopf bifurcation at the positive steady state is also discussed. By constructing a pair of upper–lower solutions and by using the cross-iteration method as well as the Schauder's fixed-point theorem, the existence of a traveling wave solution connecting the semi-trivial steady state and the positive steady state is proved. Numerical simulations are carried out to illustrate the main theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

This paper aims to present a general framework of the quadratic spline functions to develop a numerical method for solving the nonlinear space fractional Fisher's equation. Using Von Neumann method, the proposed method is shown to be conditionally stable. Finally, a numerical example is given to verify the effectiveness of the proposed algorithm. The results reveal that the proposed approach is very effective, convenient, and quite accurate to such considered problems. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we focus on the Schrodinger–Kirchhoff-type equation (SK) where a,b > 0 are constants, may not be radially symmetric, and f(x,u) is asymptotically linear with respect to u at infinity. Under some technical assumptions on V and f, we prove that the problem (SK) has a positive solution. Copyright © 2013 John Wiley & Sons, Ltd.

In the present paper, we deal with the existence and multiplicity of nontrivial solutions for a class of polyharmonic elliptic systems with Sobolev critical exponent in a bounded domain. Some new existence and multiplicity results are obtained. Our proofs are based on the Nehari manifold and Ljusternik–Schnirelmann theory. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we introduce the definition of complex complete synchronization (CCS) of hyperchaotic complex nonlinear systems that have not been introduced recently in the literature. This type of synchronization can study only for complex nonlinear systems. On the basis of Lyapunov function, a scheme is designed to achieve the CCS of two nonidentical hyperchaotic attractors of these systems. The effectiveness of the obtained results is illustrated by a simulation example. Numerical results are plotted to show state variables, modules errors, and phases errors of these hyperchaotic attractors after synchronization to prove that CCS is achieved. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we introduce systems of Volterra integral forms of the Lane–Emden equations. We use the systematic Adomian decomposition method to handle these systems of integral forms. The Volterra integral forms overcome the singular behavior at the origin x = 0. The Adomian decomposition method gives reliable algorithm for analytic approximate solutions of these systems. Our results are supported by investigating several numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.

This paper is concerned with the eigenvalues of the Neumann Laplacian on various classes of domains of given measure: simply-connected Lipschitz planar domains, n-sided planar polygons and smooth N-dimensional domains. In each case, we consider some quantities involving low eigenvalues of the Neumann Laplacian for which we obtain new inequalities. Moreover, we sharpen a universal bound derived by M. Ashbaugh and R. Benguria for sum of reciprocal of Neumann eigenvalues. Our investigations make use of some properties of conformal mappings, Bessel functions, symmetric domains or some isoperimetric inequalities for moments of inertia. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we study the existence of solutions for damped nonlinear impulsive differential equations with Dirichlet boundary conditions. By using critical point theory and variational methods, we give some new criteria to guarantee that the impulsive problems have at least one solution. Some recent results are extended and significantly improved. Finally, some examples are presented to illustrate our main results. Copyright © 2013 John Wiley & Sons, Ltd.

This paper is concerned with the large time behavior of solutions of the Cauchy problem to the one-dimensional compressible fluid models of Korteweg type, which governs the motions of the compressible fluids with internal capillarity. When the corresponding Riemann problem for the Euler system admits a contact discontinuity wave, it is shown that the viscous contact wave corresponding to the contact discontinuity is asymptotically stable provided that the strength of contact discontinuity and the initial perturbation are suitably small. The analysis is based on the elementary L2-energy method together with continuation argument. Copyright © 2013 John Wiley & Sons, Ltd.

In this paper, we study the 2D Benard problem, a system with the Navier–Stokes equations for the velocity field coupled with a convection–diffusion equation for the temperature, in an arbitrary domain (bounded or unbounded) satisfying the Poincare inequality with nonhomogeneous boundary conditions and nonautonomous external force and heat source. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal finite-dimensional pullback Dσ-attractor for the process associated to the problem. Copyright © 2013 John Wiley & Sons, Ltd.