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In this paper, we prove the local-in-time existence and a blow-up criterion of solutions in the Besov spaces for the Euler-α equations of inviscid incompressible fluid flows in Rd,d≥2. We also establish the convergence rate of the solutions of the Euler-α equations to the corresponding solutions of the Euler equations as the regularization parameter α approaches 0 in R2. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, the stochastic stability under small Gauss type random excitation is investigated theoretically and numerically. When p is larger than 0, the p-moment stability theorem of stochastic models is proved by Lyapunov method, Ito isometry formula, matrix theory and so on. Then the application of p-moment such as k-order moment of the origin and k-order moment of the center is introduced and analyzed. Finally, p-moment stability of the power system is verified through the simulation example of a one machine and infinite bus system. Copyright © 2016 John Wiley & Sons, Ltd.

The main work is related to show the existence and uniqueness of solution for the fractional impulsive differential equation of order α∈(1,2) with an integral boundary condition and finite delay. Using the application of the Banach and Sadovaskii fixed-point theorems, we obtain the main results. An example is presented at the end to verify the results of the paper. Copyright © 2016 John Wiley & Sons, Ltd.

The paper presents a novel view on the scattering of a flexural wave in a Kirchhoff plate by a semi-infinite discrete system. Blocking and channelling of flexural waves are of special interest. A quasi-periodic two-source Green's function is used in the analysis of the waveguide modes. An additional "effective waveguide" approximation has been constructed. Comparisons are presented for these two methods in addition to an analytical solution for a finite truncated system.

The aim of this paper is to propose mixed two-grid finite difference methods to obtain the numerical solution of the one-dimensional and two-dimensional Fitzhugh–Nagumo equations. The finite difference equations at all interior grid points form a large-sparse linear system, which needs to be solved efficiently. The solution cost of this sparse linear system usually dominates the total cost of solving the discretized partial differential equation. The proposed method is based on applying a family of finite difference methods for discretizing the spatial and time derivatives. The obtained system has been solved by two-grid method, where the two-grid method is used for solving the large-sparse linear systems. Also, in the proposed method, the spectral radius with local Fourier analysis is calculated for different values of h and Δt. The numerical examples show the efficiency of this algorithm for solving the one-dimensional and two-dimensional Fitzhugh–Nagumo equations. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we consider a class of nonlinear fractional differential equations on the infinite interval D0+αu(t)+ft,u(t),D0+α−1u(t)=0,t∈(0,+∞), with the integral boundary conditions u(0)=0,D0+α−1u(∞)=∫0τg1(s)u(s)ds+a,D0+α−2u(0)=∫0τg2(s)u(s)ds+b. By using Krasnoselskii fixed point theorem, the existence results of positive solutions for the boundary value problem in three cases τ=0,τ∈(0,+∞) and τ=+∞, are obtained, respectively. We also give out two corollaries as applications of the existence theorems and some examples to illustrate our results. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, numerical solutions of fractional Fokker–Planck equations with Riesz space fractional derivatives have been developed. Here, the fractional Fokker–Planck equations have been considered in a finite domain. In order to deal with the Riesz fractional derivative operator, shifted Grunwald approximation and fractional centred difference approaches have been used. The explicit finite difference method and Crank–Nicolson implicit method have been applied to obtain the numerical solutions of fractional diffusion equation and fractional Fokker–Planck equations, respectively. Numerical results are presented to demonstrate the accuracy and effectiveness of the proposed numerical solution techniques. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we study the following quasilinear Schrodinger equations: where Ω is a bounded smooth domain of , . Under some suitable conditions, we prove that this equation has three solutions of mountain pass type: one positive, one negative, and sign-changing. Furthermore, if g is odd with respect to its second variable, this problem has infinitely many sign-changing solutions. Copyright © 2016 John Wiley & Sons, Ltd.

We consider the Cauchy problem for the third-order nonlinear Schrodinger equation where ℋ=F−1iξξ−1F and F is the Fourier transform. Our purpose in this paper is to prove the large time asymptoitic behavior of solutions for the defocusing case λ > 0 with a logarithmic correction under the non zero mass condition ∫u0xdx≠0. Copyright © 2016 John Wiley & Sons, Ltd.

This paper deals with the existence and multiplicity of symmetric solutions for a class of singular quasilinear elliptic systems with critical homogeneous nonlinearity in a bounded symmetric domain. Applying variational methods and the symmetric criticality principle of Palais, we establish several existence and multiplicity results of G-symmetric solutions under some appropriate assumptions on the weighted functions and the parameters. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, boundary integral formulations for a time-harmonic acoustic scattering-resonance problem are analyzed. The eigenvalues of eigenvalue problems resulting from boundary integral formulations for scattering-resonance problems split in general into two parts. One part consists of scattering-resonances, and the other one corresponds to eigenvalues of some Laplacian eigenvalue problem for the interior of the scatterer. The proposed combined boundary integral formulations enable a better separation of the unwanted spectrum from the scattering-resonances, which allows in practical computations a reliable and simple identification of the scattering-resonances in particular for non-convex domains. The convergence of conforming Galerkin boundary element approximations for the combined boundary integral formulations of the resonance problem is shown in canonical trace spaces. Numerical experiments confirm the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we study a mathematical model of nonlinear thermoelastic wave propagation in fluid-saturated porous media, considering memory effect in the heat propagation. In particular, we derive the governing equations in one dimension by using the Gurtin–Pipkin theory of heat flux history model and specializing the relaxation function in such a way to obtain a fractional Erdelyi–Kober integral. In this way, we obtain a nonlinear model in the framework of time-fractional thermoelasticity, and we find an explicit analytical solution by means of the invariant subspace method. A second memory effect that can play a significant role in this class of models is parametrized by a generalized time-fractional Darcy law. We study the equations obtained also in this case and find an explicit traveling wave type solution. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we consider the well-posedness of a one-dimensional transport equation with nonlocal velocity in the Lei–Lin space Xs(R). We first modify the product estimate and then establish the global existence of solutions to the Cauchy problem with small enough initial data. Finally, we discuss the stability of the global solution. Copyright © 2016 John Wiley & Sons, Ltd.

This paper presents a numerical method for shape optimization of a body immersed in an incompressible viscous flow governed by Stokes–Oseen equations. The purpose of this work is to optimize the shape that minimizes a given cost functional. Based on the continuous adjoint method, the shape gradient of the cost functional is derived by involving a Lagrangian functional with the function space parametrization technique. Then, a gradient-type algorithm is applied to the shape optimization problem. The numerical examples indicate the proposed algorithm is feasible and effective in low Reynolds number flow. Copyright © 2016 John Wiley & Sons, Ltd.

In the present paper, our aim is to establish several formulas involving integral transforms, fractional derivatives, and a certain family of extended generalized hypergeometric functions. As corollaries and consequences, many interesting results are shown to follow from our main results. A probability density function involving the extended generalized hypergeometric function is introduced, and its properties are studied. The corresponding properties of some of the classical probability distributions and their associated probability density functions are easily derivable as special cases of our general results. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we study the zero viscosity and capillarity limit problem for the one-dimensional compressible isentropic Navier–Stokes–Korteweg equations when the corresponding Euler equations have rarefaction wave solutions. In the case that either the effects of initial layer are ignored or the rarefaction waves are smooth, we prove that the solutions of the Navier–Stokes–Korteweg equation with centered rarefaction wave data exist for all time and converge to the centered rarefaction waves as the viscosity and capillarity number vanish, and we also obtain a rate of convergence, which is valid uniformly for all time. These results are showed by a scaling argument and elementary energy analysis. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we show the existence and uniqueness results for periodic solutions of Weyl fractional order integral systems. A numerical example is given to illustrate our theoretical results. Our results show that periodic orbits can be obtained by putting the periodic conditions to some certain fractional order integral systems. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with the existence and uniqueness of time periodic solutions in the whole-space RN for a heat equation with nonlinear term. The nonlinear term we considered is of this type, |u|q − 1u + f(x,t), with q>NN−2, N > 2. We show that there exists a unique time periodic solution when the source term f is small. In fact, NN−2 is a critical exponent; when 1

The main objective of this paper was to study the global stability of the positive solutions and the periodic character of the difference equation xn+1=axn−l+bxn−k+cxn−sdxn−s−e,n=0,1,..., where the parameters a, b, c, d, and e are positive real numbers and the initial conditions x−t,x−t + 1,...,x−1, x0 are positive real numbers where t = max{l,k,s}. Some numerical examples will be given to explicate our results. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with the existence of positive solutions to a class of nonlocal boundary value problem of the p-Kirchhoff type {-M ( x,integral(ohm) vertical bar del u vertical bar(Rho) dx). Delta(Rho)u= f(x,u,vertical bar del u vertical bar(p-2) del)+lambda g(x,u)in(ohm)on(partial derivative ohm)vertical bar wuis a bounded smooth domain andM, f, and g are continuous functions. The existence of a positive solution is stated through an iterative method based onmountain pass theorem. Copyright (C) 2016 JohnWiley & Sons, Ltd.

In this paper, we are concerned with the system of the non-isentropic compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in three space dimensions. The global existence of solutions near constant steady states is established, and the time-decay rates of perturbed solutions are obtained. The proof for existence is due to the classical energy method, and the investigation of large-time behavior is based on the linearized analysis of the non-isentropic Navier-Stokes-Poisson equations and the electromagnetic part for the linearized isentropic Navier-Stokes-Maxwell equations. In the meantime, the time-decay rates obtained by Zhang, Li, and Zhu~[{\it J. Differential Equations, 250(2011), 866-891}] for the linearized non-isentropic Navier-Stokes-Poisson equations are improved.

This paper is concerned with the following Schrodinger elliptic system where the potential V is periodic and 0 lies in a gap of the spectrum of −Δ+V, f(x,t) and g(x,t) are superlinear in t at infinity. By using non-Nehari manifold method developed recently by Tang, we demonstrate the existence of the ground state solutions of Nehari-Pankov type for the above problem with periodic and asymptotically periodic nonlinearity. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we introduced a summation-integral type modification of Szasz–Mirakjan operators. Calculation of moments, density in some space, a direct result and a Voronvskaja-type result, are obtained. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with the mathematical analysis of the electromagnetic wave scattering by an unbounded dielectric medium, which is mounted on a perfectly conducting infinite plane. By introducing a transparent boundary condition on a plane surface confining the medium, the scattering problem is modeled as a boundary value problem of Maxwell's equations. Based on a variational formulation, the problem is shown to have a unique weak solution for a wide class of dielectric permittivity and magnetic permeability by using the generalized Lax–Milgram theorem. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, a delayed Cohen–Grossberg neural network with diffusion under homogeneous Neumann boundary conditions is investigated. By analyzing the corresponding characteristic equation, the local stability of the trivial uniform steady state and the existence of Hopf bifurcation at the trivial steady state are established, respectively. By using the normal form theory and the center manifold reduction of partial function differential equations, formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we study a cantilevered Euler–Bernoulli beam fixed to a base in a translational motion at one end and to a tip mass at its free end. The beam is subject to undesirable vibrations, and it is made of a viscoelastic material that permits a certain weak damping. By applying a control force at the base, we shall attenuate these vibrations in a fast manner. In fact, we establish the exponential stability of the system. Our method is based on the multiplier technique. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we study a multiphasic incompressible fluid model, called the Kazhikhov–Smagulov model, with a particular viscous stress tensor, introduced by Bresch and co-authors, and a specific diffusive interface term introduced for the first time by Korteweg in 1901. We prove that this model is globally well posed in a 3D bounded domain. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we consider the one-dimensional Schrodinger operator on bounded time scales. We construct a space of boundary values of the minimal operator and describe all maximal dissipative, maximal accretive, self-adjoint, and other extensions of the dissipative Schrodinger operators in terms of boundary conditions. In particular, using Lidskii's theorem, we prove a theorem on completeness of the system of root vectors of the dissipative Schrodinger operators on bounded time scales. Copyright © 2016 John Wiley & Sons, Ltd.

This paper deals with constructing generalized ‘fractional’ power series representation for solutions of fractional order differential equations. We present a brief review of generalized Taylor's series and generalized differential transform methods. Then, we study the convergence of fractional power series. Our emphasis is to address the sufficient condition for convergence and to estimate the truncated error. Numerical simulations are performed to estimate maximum absolute truncated error when the generalized differential transform method is used to solve non-linear differential equations of fractional order. The study highlights the power of the generalized differential transform method as a tool in obtaining fractional power series solutions for differential equations of fractional order. Copyright © 2016 John Wiley & Sons, Ltd.

We point out some mistakes in a known paper. Some existence results for solutions of two classes of boundary value problems for nonlinear impulsive fractional differential equations are established. Our analysis relies on the well-known Schauder fixed point theorem. Examples are given to illustrate the main results. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we establish some new sufficient conditions on the existence of homoclinic solution for a class of second-order impulsive Hamiltonian systems. By using the mountain pass theorem, we demonstrate that the limit of a 2kT-periodic approximation solution is a homoclinic solution of our problem. We also present some examples to illustrate the applications of our main results. Copyright © 2016 John Wiley & Sons, Ltd.

This paper deals with the existence of positive solutions of the discrete counterpart of nonlinear elliptic problems. We apply our methods to the study of positive solutions under different hypotheses about the nonlinearities. For example, we consider the cases that are superlinear and sublinear at infinity. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we establish new Hartman–Wintner-type inequalities for a class of nonlocal fractional boundary value problems. As an application, we obtain a lower bound for the eigenvalues of corresponding equations. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, a nonperiodic discrete nonlinear equation with Jacobi operators is considered. By using the critical point theory, we establish some new sufficient conditions on the existence and multiplicity of homoclinic solutions. Recent results are generalized and significantly improved. Furthermore, our results greatly improve some existing ones even for some special cases. Copyright (c) 2016 John Wiley & Sons, Ltd.

A dimension splitting method (DSM) with Crank–Nicolson time discrete strategy for a three-dimensional heat equation is proposed. The basic idea is to simulate the three-Dimensional problem by numerically solving a series of two-dimensional problems in parallel fashion. Convergence and error estimation for the DSM scheme are derived in the paper. Numerical experiments demonstrate the feasibility and efficiency of the DSM scheme. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with the control systems of semilinear fractional evolution hemivariational inequalities and their optimal controls in Banach space. Firstly, the existence of mild solutions is obtained and proved mainly by using a well-known fixed point theorem of multivalued maps and the properties of generalized Clarke subdifferential. Then, by applying generally mild conditions of cost functionals, we investigate the existence results of the optimal controls for fractional differential evolution hemivariational inequalities. Finally, an example is given to demonstrate the applicability of the main results. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with the regularity criterion for a class of axisymmetric solutions to 3D incompressible magnetohydrodynamic equations. More precisely, for the solutions that have the form of u = urer+uθeθ+uzez and b = bθeθ, we prove that if |ru(x,t)|≤C holds for −1≤t < 0, then (u,b) is regular at time zero. This result can be thought as a generalization of recent results in for the 3D incompressible Navier-Stokes equations. Copyright © 2016 John Wiley & Sons, Ltd.

An optimal boundary control problem in a domain with oscillating boundary has been investigated in this paper. The controls are acting periodically on the oscillating boundary. The controls are applied with suitable scaling parameters. One of the major contribution is the representation of the optimal control using the unfolding operator. We then study the limiting analysis (homogenization) and obtain two limit problems according to the scaling parameters. Another notable observation is that the limit optimal control problem has three controls, namely, a distributed control, a boundary control, and an interface control. Copyright (C) 2016 John Wiley & Sons, Ltd.

This paper discusses the problem of stability and periodic behaviour of linear planar difference systems appearing in modelling of discrete problems of population biology and Hopfield neural networks. We concentrate especially on procedures, which enable to formulate optimal (i.e. necessary and sufficient) conditions guaranteing such a behaviour. As a main tool, we analyse in detail location of zeros of characteristic polynomials with respect to the unit circle. From this viewpoint, derived results contribute also to the polynomial theory. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we give an alternative proof to the global existence result, which is originally owing to the pioneering work of Klainerman and Christodoulou, for the Cauchy problem of quasilinear wave equations with null condition in three space dimensions. The proof can display the following three features simultaneously: the Lorentz boost operator is not employed in the generalized energy estimates; the generalized energy of the solution will be always small, which was first observed by Alinhac; and the initial data are not assumed to have a compact support. Copyright © 2016 John Wiley & Sons, Ltd.

The paper investigates an extension of the coupled integrable dispersionless equations, which describe the current-fed string within an external magnetic field. By using the relation among the coupled integrable dispersionless equations, the sine-Gordon equation and the two-dimensional Toda lattice equation, we propose a generalized coupled integrable dispersionless system. N-soliton solutions to the generalized system are presented in the Casorati determinant form with arbitrary parameters. By choosing real or complex parameters in the Casorati determinant, the properties of one-soliton and two-soliton solutions are investigated. It is shown that we can obtain solutions in soliton profile and breather profile. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we study the following biharmonic equation where , K(1) > 0,K′(1) > 0, B1(0) is the unit ball in (N≥6). We show that the aforementioned problem has infinitely many peak solutions, whose energy can be made arbitrarily large. Copyright © 2016 John Wiley & Sons, Ltd.

This paper studies the local-in-time existence of classical solutions to a hyperbolic system with differential boundary conditions modelling a flow in an elastic tube. The well-known Lax transformations used for obtaining a priori estimates for conservation laws are difficult to apply here because of the inhomogeneity of the partial differential equations (PDE). Rather, our method relies on a suitable splitting of the original system into the PDE part and the ODE part, the characteristics for the PDE part, appropriate modulus of continuity estimates and a compactness argument. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we consider a variable coefficient Calogero–Degasperis equation, a variable coefficient potential Kadomstev–Petviashvili equation and the generalized (3+1)-dimensional variable coefficient Kadomtsev–Petviashvili equation with time-dependent coefficients. Shock wave solutions for the considered models are obtained by using ansatz method in the form of tanhp function. The physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we employ the method of lower and upper solutions coupled with the monotone iterative technique to obtain existence and uniqueness of extremal mild solutions to neutral fractional differential equation with infinite delay in an ordered Banach space. The results are obtained by using the theory of fractional calculus, monotone iterative technique, measure of noncompactness, and semigroup theory. Finally, we discuss an example to illustrate our results. Copyright © 2016 John Wiley & Sons, Ltd.

The aim of this paper is to establish a continuation principle for strong solutions to the full compressible magnetohydrodynamic system without resistivity and heat conductivity. We prove that if the solution loses its regularity in finite time, the dominated part is due to the hyperbolic effect. More precisely, it is essentially shown that the strong solution exists globally if the density, temperature, and magnetic field are bounded from above, where vacuum is allowed to exist. This verifies a problem proposed by D.Serre. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is concerned with a class of non-autonomous neutral functional differential equations with multi-proportional delays. It is shown that all solutions of the addressed system are globally exponentially convergent by employing the differential inequality technique and a novel argument. The obtained results improve and supplement existing ones. We also use numerical simulations to demonstrate our theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we study the stability of the zero equilibria of the following systems of difference equations: and where a, b, c and d are positive constants and the initial conditions x0 and y0 are positive numbers. We study the stability of those systems in the special case when one of the eigenvalues has absolute value equal to 1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. Copyright © 2016 John Wiley & Sons, Ltd.

The main object of this paper is to extend some known approximation results for the complex beta operators of the first kind attached to analytic functions in strips of compact disks. The extensions of these approximation properties, which are presented here, involve bicomplex beta operators in compact -disk. Several other related results are also considered. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we investigate the vanishing viscosity limit problem for the 3D incompressible magnetohydrodynamic (MHD) system in a general bounded smooth domain of R3 with the generalized Navier slip boundary conditions. We also obtain rates of convergence of the solution of viscous MHD to the corresponding ideal MHD. Copyright © 2016 John Wiley & Sons, Ltd.