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In this paper, we will analyze further to obtain a finer asymptotic behavior of positive solutions of semilinear elliptic equations in ℝ n by employing the Li’s method of energy function. [ABSTRACT FROM AUTHOR]

In this paper we study the a one-dimensional reaction-diffusion-convection (R-D-C) equation with weak spatial non-uniformities to the diffusion and reaction rates. The convection is represented by a uniform flow field. Singular perturbation analysis will be used to compute the speed of the front as well as the asymptotic solution. [ABSTRACT FROM AUTHOR]

The goal of this paper is to derive a fluid-structure model from a three-dimensional formulation and using an asymptotic method. The mechanical model that we consider is a flow duct, a part of which is flexible. This part can be assimilated to a shell or a membrane structure and a smart device is located on it in order to control the vibrations induced by the flow inside the duct. This control model is known to be challenging and no realistic controllability result has been obtained as far as a three-dimensional model is considered. But it can be derived for one-dimensional model. It is the reason why we are interested in this paper to analyze the links between the three-dimensional model and a limit one, assuming that the duct is quite long compared to its radius. The basic tool is a scaling method in the transverse section of the duct. [ABSTRACT FROM AUTHOR]

Our aim is to investigate the global asymptotic behaviour, oscillation, periodicity and bifurcation in discontinuous Beverton–Holt type difference equationwherex0>0, functionskandrare discontinuous piecewise constant functionssatisfyingandhis Heaviside function. [ABSTRACT FROM AUTHOR]

The boundedness character of positive solutions of the following cyclic system of difference equationswhereA,pandqare positive numbers, and where if, for someand, thendenotes, is completely described in this paper. [ABSTRACT FROM AUTHOR]

In this paper we study the asymptotic behaviour of the positive solutions of the system of two difference equationswhereare positive constants and the initial valuesare positive numbers. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new method to construct explicit bounds for the solutions of second order linear differential equations of the type ,, , which complements the method described in recent papers of the authors. The method lies in the use of Beesack’s version of Opial’s inequality. Some results on asymptotics of the solution for the case are also included. [Copyright &y& Elsevier]

This paper is concerned with the asymptotic behavior of the solutions u(x,t) of the Swift–Hohenberg equation with quintic nonlinearity on a one-dimensional domain (0, L). With α and the length L of the domain regarded as bifurcation parameters, branches of nontrivial solutions bifurcating from the trivial solution at certain points are shown. Local behavior of these branches are also studied. Global bounds for the solutions u(x,t) are established and then the global attractor is investigated. Finally, with the help of a center manifold analysis, two types of structures in the bifurcation diagrams are presented when the bifurcation points are closer, and their stabilities are analyzed. [ABSTRACT FROM AUTHOR]

We continue our previous study of sharp Sobolev-type inequalities by means of optimal transport, started in (Maggi and Villani J. Geom. Anal. 15(1), 83–121 (2005)). In the present paper, we extend our results in various directions, including Gagliardo–Nirenberg, Faber–Krahn, logarithmic-Sobolev or Moser–Trudinger inequalities with trace terms. We also identify a class of domains for which there is no need for a trace term to cast the Sobolev inequality. [ABSTRACT FROM AUTHOR]

In this paper, we consider a system of two cubic quasi–linear Klein–Gordon equations with different masses for small, smooth, compactly supported Cauchy data in one space dimension. We show that such a system has global existence when the nonlinearities satisfy a convenient null condition. Our results extend the global existence proved by Sunagawa recently under the non–resonance assumption to that under the resonance assumption. [ABSTRACT FROM AUTHOR]

In this paper we study ergodic properties of hidden Markov models with a generalized observation structure. In particular sufficient conditions for the existence of a unique invariant measure for the pair filter-observation are given. Furthermore, necessary and sufficient conditions for the existence of a unique invariant measure of the triple state-observation-filter are provided in terms of asymptotic stability in probability of incorrectly initialized filters. We also study the asymptotic properties of the filter and of the state estimator based on the observations as well as on the knowledge of the initial state. Their connection with minimal and maximal invariant measures is also studied. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to investigate the asymptotic behavior of solutions of the following difference equation [This symbol cannot be presented in ASCII format] where {an} is a positive bounded sequence and k is a positive integer. Sufficient conditions for boundedness and attractivity are obtained. The results are applied to the special case when {an} is a periodic sequence with prime period p. [ABSTRACT FROM AUTHOR]

The paper is devoted to asymptotic analysis of the mathematical model of two-composite materials. The main result is the deduction of the extended Stefan problem being a singular limit of the initial problem. [ABSTRACT FROM AUTHOR]

Abstract: It is the goal of this paper to study the boundedness, the persistence and the asymptotic behavior of the positive solutions of the system of two difference equations of exponential form where are positive constants, and the initial values are positive real values. [Copyright &y& Elsevier]

The paper is concerned with the analysis of a new class of overlapping domain problems for elastic bodies having cracks. Inequality type boundary conditions are imposed on the crack faces. We prove an existence of invariant integrals and analyze the asymptotic behavior of the solution. It is shown that the limit problem describes an equilibrium state for the elastic body with a thin inclusion. [ABSTRACT FROM AUTHOR]

Time scales have been introduced in order to unify the theories of differential and difference equations and in order to extend these cases to many other so-called dynamic equations. In this paper we consider a linear dynamic equation on a time scale together with a perturbed equation. We show that, if certain exponential dichotomy conditions are satisfied, then for any solution of the perturbed equation there exists a solution of the unperturbed equation that asymptotically differs from the solution of the perturbed equation no more than the order of the perturbation term. In order to show this perturbation theorem, we use many properties of the exponential function on time scales and derive several bounds for certain monomials that appear in the dynamic version of Taylor's formula. [ABSTRACT FROM AUTHOR]

We consider the large time asymptotic behavior of solutions to the initial-boundary value problem [This symbol cannot be presented in ASCII format]. We find large time asymptotic formulas of solutions for three different cases 1) a± = ±1, 2) a± = [This symbol cannot be presented in ASCII format]1 and 3) a± = 0. [ABSTRACT FROM AUTHOR]

In construction asymptotic solutions of equations describing waves concentrated near moving lines or surfaces, special solutions (also asymptotic) of the Hamilton Jacobi equation play a central role. These solutions are real on a certain surface and are complex outside it. Solutions of such a type have been considered for the first time by V. P. Maslov. To give a mathematical description of some types waves not considered earlier, the authors return to solutions of the Hamilton Jacobi equations. For the applications that are kept in mind, it is necessary to describe thoroughly constructions, which lead to the required solution of the Hamilton-Jacobi equation in a proper form. This paper is devoted to such a description. Bibliography: 3 titles. [ABSTRACT FROM AUTHOR]

We show that the following system of difference equationswhere,,, and sequences,,andare real, can be solved in closed form. For the case when the sequences,,andare constant and, we apply obtained formulas in the investigation of the asymptotic behaviour of well-defined solutions of the system. We also find domain of undefinable solutions of the system. Our results considerably extend and improve some recent results in the literature. [ABSTRACT FROM AUTHOR]

The asymptotic behaviour of solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness h of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of h, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von Kármán plate equation. [ABSTRACT FROM AUTHOR]

We prove the existence and uniqueness of the solutions of a class of first order nonhomogeneous advanced impulsive differential equations with piecewise constant arguments. We also study the conditions of periodicity, oscillation, nonoscillation and global asymptotic stability for some special cases. [ABSTRACT FROM AUTHOR]

We study the equation ∂tu-Δu=up-μ |∇u|qur in a general domain (bounded or not). Many results have been established in the case r=0, and we will generalize some properties. If q≥1 and q+r≥p, we will show that there is a strong connection between the finiteness of the inradius of Ω (or the Poincaré inequality) and the global existence of the solutions. More precisely if the inradius of Ω is finite, then the solutions u are global and if moreover μ is large enough, the solutions decay exponentially to zero. Conversely, if it is infinite, there always exists unbounded solution. Other qualitative results are also obtained. [ABSTRACT FROM AUTHOR]

We prove the SH1 p —theory for critical equations involving the p-Laplace operator on compact manifolds. We also prove pointwise estimates for these equations. [ABSTRACT FROM AUTHOR]

This article deals with the links between compensated compactness and two-scale convergence. More precisely, we ask the following question: Is the div-curl compactness assumption sufficient to pass to the limit in a product of two sequences which two-scale converge with respect to the pair of variables $(x,{x/\varepsilon})$? We reply in the negative. Indeed, the div-curl assumption allows us to control oscillations which are faster than ${1/\varepsilon}$ but not the slower ones. [ABSTRACT FROM AUTHOR]

We study the stability of solutions of fuzzy differential equations by Lyapunov's second method. By using scale equations and the comparison principle for Lyapunov-like functions, we give sufficient criteria for the stability and asymptotic stability of solutions of fuzzy differential equations. [ABSTRACT FROM AUTHOR]

A detailed description is given on the large time behavior of scattering solutions to the Cauchy problem for nonlinear Schrödinger equations with repulsive interactions in the short-range case without smallness condition on the data. [ABSTRACT FROM AUTHOR]

In this article, we study conditions for the asymptotic equivalence of differential equations in Hilbert spaces. We also discuss the relationship between the properties of solutions of differential equations of triangular form and those of truncated differential equations. [ABSTRACT FROM AUTHOR]

We consider a classical problem of free oscillations of the elastic weightless string with N + 1 beads which has been originally studied by Lagrange. It is proved that for N being prime or a power of 2, the maximal displacement of the bead from its equilibrium position increases logarithmically to infinity as N → ∞. [ABSTRACT FROM AUTHOR]

The multidimensional renewal equation ϕ(t) = g(t) + ∫0t [dF (x)] ϕ(t - x) is considered. Here g ∈ L1n(0; ∞), F(t) = (Fij (t))i,j=1n (n < ∞), F(t) = 0 for t ≦ 0, F(t) ↑, r(A) = 1, where A = F(+∞) and r(A) is the spectral radius of the matrix A. For the particular case of the Markov renewal equation ∫i=1n Fij(+∞) = 1. We assume that A is an indecomposable matrix and a convolution power of the measure dF has a nontrivial absolutely continuous component. Under these conditions it is shown that the solution of the Markov renewal equation has the form: ϕ(t) = μ+ρ(t)+ψ(t), ρ ∈ C0n [0;∞), ψ ∈ L1n (0;∞). If dF is a measure with finite second moment, then ρ ∈ L1n (0;∞). Explicit formulas are obtained for μ and σ = ∫0∞ [ϕ(t) - μ]dt. Hence there follows, in particular, an asymptotic formula for ∫0t ϕ(x) dx. [ABSTRACT FROM AUTHOR]

We consider a random walk {Sn} with dependent heavy-tailed increments and negative drift. We study the asymptotics for the tail probability P{supnSn>x} as x→∞. If the increments of {Sn} are independent then the exact asymptotic behavior of P{supnSn>x} is well known. We investigate the case in which the increments are given as a one-sided asymptotically stationary linear process. The tail behavior of supnSn turns out to depend heavily on the coefficients of this linear process. [ABSTRACT FROM AUTHOR]