共查询到20条相似文献,搜索用时 5 毫秒
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A. Salvatore 《Journal of Differential Equations》2008,244(10):2529-2544
We prove the existence of infinitely many solutions for symmetric elliptic systems with nonlinearities of arbitrary growth. Moreover, if the symmetry of the problem is broken by a small enough perturbation term, we find at least three solutions. The proofs utilise a variational setting given by de Figueiredo and Ruf in order to prove an existence's result and the “algebraic” approach based on the Pohozaev's fibering method. 相似文献
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João M. Bezerra do Ó Olímpio H. Miyagaki Sérgio H.M. Soares 《Journal of Differential Equations》2010,248(4):722-744
In this paper we establish the existence of standing wave solutions for quasilinear Schrödinger equations involving critical growth. By using a change of variables, the quasilinear equations are reduced to semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the geometric conditions of the mountain pass theorem. Using this fact, we obtain a Cerami sequence converging weakly to a solution v. In the proof that v is nontrivial, the main tool is the concentration-compactness principle due to P.L. Lions together with some classical arguments used by H. Brezis and L. Nirenberg (1983) in [9]. 相似文献
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Everaldo Medeiros 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(9):3654-3660
In this paper we study a quasilinear elliptic problem with the Dirichlet boundary condition in a bounded domain involving the operator Au=−Δpu−Δqu. Assuming that the nonlinearity has a concave-convex behavior we obtain some multiplicity results. More precisely, we obtain five nontrivial solutions; two by a minimization argument, two by the mountain pass theorem, and the other by a cohomological linking theorem. 相似文献
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We prove the existence of a weak solution of the Dirichlet problem for a class of elliptic partial differential systems in separable Orlicz–Sobolev spaces. 相似文献
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Yuri Bozhkov 《Journal of Differential Equations》2003,190(1):239-267
By using the fibering method introduced by Pohozaev, we prove existence of multiple solutions for a Diriclhlet problem associated to a quasilinear system involving a pair of (p,q)-Laplacian operators. 相似文献
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We study the existence of multiple solutions for a quasilinear elliptic system of gradient type with the possibility of coupling on the critical and subcritical terms which are not necessarily homogeneous. The solutions are obtained from a version of the Symmetric Mountain Pass Theorem. A version of the Concentration-Compactness Principle for this class of systems allows us to verify that the Palais–Smale condition is satisfied below a certain level. 相似文献
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In this paper, we are concerned with the existence of sign-changing solutions of a class of nonlinear elliptic systems with critical growth. 相似文献
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In this paper we study the existence and structure of the least-energy solutions for a class of singularly perturbed quasilinear elliptic equations. Using the moving plane method and a geometric lemma we show that any least-energy solution develops to a single spike-layer solution on convex domains. 相似文献
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Bhatia Sumit Kaur 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(8):2368-2382
Let Ω be a bounded domain in RN,N≥2, with C2 boundary. In this work, we study the existence of multiple positive solutions of the following problem:
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Andrés I. Ávila Jianfu Yang 《NoDEA : Nonlinear Differential Equations and Applications》2006,12(4):459-479
We proved a multiplicity result for a nonlinear elliptic system in RN. The functional related to the system is strongly indefinite. We investigated the relation between the number of solutions
and the topology of the set of the global maxima of the coefficients. 相似文献
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This paper is concerned with the positive solutions for generalized quasilinear Schrödinger equations in RN with critical growth which have appeared from plasma physics, as well as high-power ultrashort laser in matter. By using a change of variables and variational argument, we obtain the existence of positive solutions for the given problem. 相似文献
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Kuan-Ju Chen 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):806-821
In this paper we study a multiplicity result for a strongly indefinite semilinear elliptic system
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Existence of solutions for a class of singular quasilinear elliptic resonance problems 总被引:1,自引:0,他引:1
The paper concerns a resonance problem for a class of singular quasilinear elliptic equations in weighted Sobolev spaces. The equation set studied is one of the most useful sets of Navier-Stokes equations; these describe the motion of viscous fluid substances such as liquids, gases and so on. By using Galerkin-type techniques, the Brouwer fixed point theorem, and a new weighted compact Sobolev-type embedding theorem established by Shapiro, we show the existence of a nontrivial solution. 相似文献
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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
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Alexandru Kristály 《Journal of Differential Equations》2010,249(8):1917-1928
We guarantee the existence of infinitely many different pairs of solutions to the system
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Dengfeng Lü 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6371-6382
In this paper, we study the existence and multiplicity of nontrivial solutions for a class of biharmonic elliptic systems with Sobolev critical exponent in a bounded domain. By using the variational method and the Nehari manifold, we obtain the existence and multiplicity results of nontrivial solutions for the systems. 相似文献