Multiplicity of solutions for a class of quasi- linear elliptic equation involving the critical Sobolev and Hardy exponents
نویسندگان
چکیده
In this paper, by using concentration-compactness principle and a new version of the symmetric mountain-pass lemma due to Kajikiya (J Funct Anal 225:352–370, 2005), infinitely many small solutions are obtained for a class of quasilinear elliptic equation with singular potential −∆pu− μ |u| p−2u |x|p = |u|p(s)−2u |x|s + λf(x, u), u ∈ H 1,p 0 (Ω). Mathematics Subject Classification (2000). 35J60, 35J92, 35J25.
منابع مشابه
The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent
In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.
متن کاملOn Multiple Solutions for a Singular Quasilinear Elliptic System Involving Critical Hardy-sobolev Exponents
This paper is concerned with the existence of nontrivial solutions for a class of degenerate quasilinear elliptic systems involving critical Hardy-Sobolev type exponents. The lack of compactness is overcame by using the Brezis-Nirenberg approach, and the multiplicity result is obtained by combining a version of the Ekeland’s variational principle due to Mizoguchi with the Ambrosetti-Rabinowitz ...
متن کاملQuasilinear Schrödinger equations involving critical exponents in $mathbb{textbf{R}}^2$
We study the existence of soliton solutions for a class of quasilinear elliptic equation in $mathbb{textbf{R}}^2$ with critical exponential growth. This model has been proposed in the self-channeling of a high-power ultra short laser in matter.
متن کاملON QUASILINEAR ELLIPTIC SYSTEMS INVOLVING MULTIPLE CRITICAL EXPONENTS
In this paper, we consider the existence of a non-trivial weaksolution to a quasilinear elliptic system involving critical Hardyexponents. The main issue of the paper is to understand thebehavior of these Palais-Smale sequences. Indeed, the principaldifficulty here is that there is an asymptotic competition betweenthe energy functional carried by the critical nonlinearities. Thenby the variatio...
متن کاملSolutions for the quasi-linear elliptic problems involving the critical Sobolev exponent
In this article, we study the existence and multiplicity of positive solutions for the quasi-linear elliptic problems involving critical Sobolev exponent and a Hardy term. The main tools adopted in our proofs are the concentration compactness principle and Nehari manifold.
متن کامل