共查询到20条相似文献,搜索用时 9 毫秒
1.
Existence of periodic solutions of nonlinear systems with nonlinear boundary conditions 总被引:1,自引:0,他引:1
In this paper we consider the periodic solutions of nonlinear parabolic systems with nonlinear boundary conditions. By constructing the Poincare operator, we obtain the existence of
-periodic weak solutions under some reasonable assumptions. 相似文献
2.
We consider a class of asymptotically linear nonautonomous second-order Hamiltonian systems. Using the Saddle Point Theorem, we obtain the existence result, which extends some previously known results. 相似文献
3.
Zhijun Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(16):5544-5553
We study the existence, boundary behavior and uniqueness of solutions for the singular elliptic system −Δu=u−pv−q,−Δv=u−rv−s,u>0,v>0,x∈Ω,u|∂Ω=v|∂Ω=0, where Ω is a bounded domain with smooth boundary in RN, p,s≥0 and q,r>0. Our results are obtained in a range of p,q,r,s different from those in [M. Ghergu, Lane-Emden systems with negative exponents, J. Funct. Anal. 258 (2010) 3295-3318]. 相似文献
4.
Summary We give a complete classification of the small-amplitude finite-gap solutions of the sine-Gordon (SG) equation on an interval under Dirichlet or Neumann boundary conditions. Our classification is based on an analysis of the finite-gap solutions of the boundary problems for the SG equation by means of the Schottky uniformization approach.On leave from IPPI, Moscow, Russia 相似文献
5.
A classical stationary Boussinesq system with non-homogeneous Dirichlet boundary conditions in a bounded domain is considered in this paper; included is the case of a possibly disconnected boundary. We prove existence of a weak, a strong and a very weak solution in -theory. Uniqueness of the very weak solution is proved under a small data assumption. 相似文献
6.
Manuel Pinto 《Applied mathematics and computation》2010,217(8):4167-4177
The existence and global exponential stability of an almost periodic solution of an impulsive neural network model with distributed delays is considered in a matrix setting. The approach transforms the original network into a matrix analysis problem, where a set of sufficient conditions based on spectral radius is presented. A concrete Hopfield model shows the advantages in comparison with a classical norm approach. 相似文献
7.
Laurence Cherfils 《Journal of Mathematical Analysis and Applications》2008,343(1):557-566
Our aim in this article is to prove the global (in time) existence of solutions to a Caginalp phase-field system with dynamic boundary conditions and a singular potential. The main difficulty is to prove that the solutions are strictly separated from the singular values of the potential. This is achieved by studying an auxiliary elliptic problem. 相似文献
8.
Shuqin Zhang 《Communications in Nonlinear Science & Numerical Simulation》2013,18(12):3289-3297
In this work, a differential equation of variable-order with nonlinear boundary value conditions is discussed. By some analysis techniques and Arzela–Ascoli theorem, existence result of solution is obtained. 相似文献
9.
In this article, we study the existence of nontrivial solutions for a class of asymptotically linear Hamiltonian systems with Lagrangian boundary conditions by the Galerkin approximation methods and the L-index theory developed by the first author. 相似文献
10.
Christopher C. Tisdell 《Journal of Mathematical Analysis and Applications》2006,323(2):1325-1332
This article investigates the existence of solutions to boundary value problems (BVPs) involving systems of first-order ordinary differential equations and two-point, periodic boundary conditions. The methods involve novel differential inequalities and fixed-point theory to yield new theorems guaranteeing the existence of at least one solution. 相似文献
11.
Yang Zhang 《复变函数与椭圆型方程》2015,60(7):951-967
In this paper, we investigate semilinear elliptic systems having a parameter with nonlinear Neumann boundary conditions over a smooth bounded domain. The objective of our study is to analyse bifurcation component of positive solutions from trivial solution and their stability. The results are obtained via classical bifurcation theorem from a simple eigenvalue, by studying the eigenvalue problem of elliptic systems. 相似文献
12.
The aim of this paper is to investigate the existence, uniqueness, and asymptotic behavior of solutions for a coupled system of quasilinear parabolic equations under nonlinear boundary conditions, including a system of quasilinear parabolic and ordinary differential equations. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system as well as the uniqueness of a positive steady-state solution. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients Di(ui) may have the property Di(0)=0 for some or all i. Our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. It is shown that the time-dependent solution converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a porous medium type of problem, a heat-transfer problem, and a two-component competition model in ecology. These applications illustrate some very interesting distinctive behavior of the time-dependent solutions between density-independent and density-dependent diffusions. 相似文献
13.
In this paper, we mainly introduce a general method to study the existence and uniqueness of solution of free boundary problems with partially degenerate diffusion. 相似文献
14.
Hideo Deguchi 《Monatshefte für Mathematik》2009,156(3):211-231
This paper is devoted to the study of the initial value problem for parabolic systems with discontinuous nonlinearities from
the viewpoint of the existence, uniqueness and stability of weak solutions. Also the relationship with the solutions of the
corresponding differential inclusions is studied.
相似文献
15.
A. B. Vasil’eva L. V. Kalachev 《Computational Mathematics and Mathematical Physics》2007,47(2):215-226
In this paper, we continue the analysis of alternating boundary layer type solutions to certain singularly perturbed parabolic
equations for which the degenerate equations (obtained by setting small parameter multiplying derivatives equal to zero) are
algebraic equations that have three roots. Here, we consider spatially one-dimensional equations. We address special cases
where the following are true: (a) boundary conditions are of the Dirichlet type with different values of unknown functions
specified at different endpoints of the interval of interest; (b) boundary conditions are of the Robin type with an appropriate
power of a small parameter multiplying the derivative in the conditions. We emphasize a number of new features of alternating
boundary layer type solutions that appear in these cases. One of the important applications of such equations is related to
modeling certain types of bioswitches. Special choices of Dirichlet and Robin type boundary conditions can be used to tune
up such bioswitches.
This article was submitted by the authors in English. 相似文献
16.
In this paper, we prove some sufficient conditions for the local and global existence of fractional nonlinear finite time delay evolution equations whose linear part is the infinitesimal generators of analytic semigroups. The results are obtained by applying the generalized singular versions of integral inequalities under some different conditions on nonlinear term. At last, two examples are given for demonstration. 相似文献
17.
Dan Zhang Binxiang Dai Yuming Chen 《Mathematical Methods in the Applied Sciences》2014,37(10):1538-1552
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. 相似文献
18.
19.
Yongxiang Li 《Journal of Functional Analysis》2011,261(5):1309-1324
In this paper, we discuss the existence and asymptotic stability of the time periodic solution for the evolution equation with multiple delays in a Hilbert space H
20.
M. Bogoya R. Ferreira J.D. Rossi 《Journal of Mathematical Analysis and Applications》2008,337(2):1284-1294
We deal with boundary value problems (prescribing Dirichlet or Neumann boundary conditions) for a nonlocal nonlinear diffusion operator which is analogous to the porous medium equation. First, we prove existence, uniqueness and the validity of a comparison principle for these problems. Next, we impose boundary data that blow up in finite time and study the behavior of the solutions. 相似文献