共查询到20条相似文献,搜索用时 546 毫秒
1.
Lina LüJiabao Su 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(16):5340-5351
In this paper, we study the existence and multiplicity of nontrivial solutions for a gradient system with resonance at both zero and infinity via Morse theory. 相似文献
2.
In this paper, we study existence and multiplicity of nontrivial solutions for a class of Schrödinger–Maxwell systems via variational methods. Some new existence results of nontrivial solutions are obtained. 相似文献
3.
In this paper, we study the existence and multiplicity of nontrivial periodic solutions for an asymptotically linear wave equation with resonance, both at infinity and at zero. The main features are using Morse theory for the strongly indefinite functional and the precise computation of critical groups under conditions which are more general. 相似文献
4.
Thomas Bartsch 《Journal of Differential Equations》2006,220(2):531-543
In this work, we consider semilinear elliptic systems for the polyharmonic operator having a critical growth nonlinearity. We establish conditions for existence and nonexistence of nontrivial solutions to these systems. 相似文献
5.
Dengfeng Lü 《Mathematical Methods in the Applied Sciences》2014,37(4):581-596
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. 相似文献
6.
刘朝霞 《数学物理学报(B辑英文版)》2010,30(1):55-64
Based on the multiplicity results of Benci and Fortunato [4], we consider some elliptic systems with strongly indefinite quadratic part, and establish the existence of infinitely many nontrivial solutions in a suitable family of products of fractional Sobolev spaces. 相似文献
7.
《Mathematical Methods in the Applied Sciences》2018,41(8):3197-3212
In this paper, the existence and multiplicity of nontrivial solutions are obtained for nonlinear fractional differential systems with p‐Laplacian by combining the properties of fractional calculus with critical point theory. Firstly, we present a result that a class of p‐Laplacian fractional differential systems exists infinitely many solutions under the famous Ambrosetti‐Rabinowitz condition. Then, a criterion is given to guarantee that the fractional systems exist at least 1 nontrivial solution without satisfying Ambrosetti‐Rabinowitz condition. Our results generalize some existing results in the literature. 相似文献
8.
Zeng-Qi Ou 《Journal of Mathematical Analysis and Applications》2011,383(2):423-438
The existence and multiplicity of nontrivial solutions are obtained for the quasilinear elliptic systems by the linking argument, the cohomological index theory and the pseudo-index theory. 相似文献
9.
Shiwang Ma 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(12):3856-3872
In this paper, we consider a class of resonant cooperative elliptic systems. Based on some new results concerning the computations of the critical groups and the Morse theory, we establish some new results about the existence and multiplicity of solutions under new classes of conditions. It turns out that our main results sharply improve some known results in the literature. 相似文献
10.
Multiple solutions for fourth-order boundary value problem 总被引:4,自引:0,他引:4
In this paper, we study the existence and multiplicity of nontrivial solutions for the fourth-order two point boundary value problems. Making use of the theory of fixed point index in cone and Leray-Schauder degree, under general conditions on nonlinearity, we prove that there exist at least six different nontrivial solutions for the fourth-order two point boundary value problems. Furthermore, if the nonlinearity is odd, we obtain that there exist at least eight different nontrivial solutions. 相似文献
11.
本文主要研究2n阶两点边值问题的多重非平凡解的存在性.利用不动点指数理论和Leray-schauder度,在一般的非线性条件下,证明了2n阶两点边值问题至少有六个非平凡解的存在性.而且,如果非线性项是奇函数,则至少有八个非平凡解的存在. 相似文献
12.
13.
Boris Buffoni Alexander Mielke 《Calculus of Variations and Partial Differential Equations》2001,13(4):469-489
We consider the minimization problem for the functional where is an infinitely long cylinder. The density is polyconvex and assumed to be 0 on a set of wells and positive elsewhere. We show that the gradients of solutions with finite energy have to approach one component
for and one component for , if the number of components is finite (among other conditions). Moreover, for certain pairs of distinct components we construct
nontrivial minimizers within the class of solutions approaching the given components. We follow ideas developed in the variational
study of heteroclinic connections for Lagrangian systems and we put special emphasis on multiplicity of such interface solutions.
We discuss an application in the theory of nonlinear elasticity, where such solutions are called semi-necks. When a two-dimensional infinite hyperelastic strip is stretched along its infinite direction it may occur that for a given
tensile load many homogeneous deformations are possible. In such a case we show by infimizing the energy functional the existence
of configurations that tend asymptotically to two different homogeneous deformations.
Received: 1 March 2000 / Accepted: 4 December 2000 / Published online: 4 May 2001 相似文献
14.
Gianni Arioli 《Journal of Differential Equations》2007,235(1):298-307
We study a reaction-diffusion system of two parabolic differential equations describing the behavior of a nuclear reactor. We provide existence results for nontrivial periodic solutions, nonexistence results for stationary solutions and we prove that, depending on the value of the parameters, either the system admits a compact global attractor, or the solutions are unbounded. 相似文献
15.
Marcos Montenegro 《Journal of Differential Equations》2009,247(3):906-3417
In the present work, we consider elliptic systems involving polyharmonic operators and critical exponents. We discuss the existence and nonexistence of nontrivial solutions to these systems. Our theorems improve and/or extend the ones established by Bartsch and Guo [T. Bartsch, Y. Guo, Existence and nonexistence results for critical growth polyharmonic elliptic systems, J. Differential Equations 220 (2006) 531-543] in both aspects of spectral interaction and regularity of lower order perturbations. 相似文献
16.
《Applied Mathematics Letters》2005,18(4):439-444
We study the existence and multiplicity of nontrivial periodic solutions for a semilinear fourth-order ordinary differential equation arising in the study of spatial patterns for bistable systems. Variational tools such as the Brezis–Nirenberg theorem and Clark theorem are used in the proofs of the main results. 相似文献
17.
We study the existence of nontrivial radial solutions for quasilinear elliptic equations with unbounded or decaying radial potentials. The existence results are based upon several new embedding theorems we establish in the paper for radially symmetric functions. 相似文献
18.
In this note, we study the existence and multiplicity of solutions for a system of coupled elliptic equations. We introduce a revised Ambrosetti–Rabinowitz condition, and show that the system has a nontrivial solution or even infinitely many solutions. 相似文献
19.
In this paper, we consider the existence and multiplicity of homoclinic type solutions to a system of diffusion equations with spectrum point zero. By using some recent critical point theorems for strongly indefinite problems, we obtain at least one nontrivial solution and also infinitely many solutions. 相似文献
20.
This paper concerns the existence and multiplicity of solutions of second-order difference boundary value problems. Under
the assumptions which guarantee the existence of at least one nontrivial solution of the homogeneous problem, we obtain the
existence of exactly three solutions of the nonhomogeneous problem with some other suitable conditions. 相似文献