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The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent

Journal: Sahand Communications in Mathematical Analysis (Vol.12, No. 1)

Publication Date:

Authors : ; ;

Page : 39-57

Keywords : Variational methods; Nehari manifold; Dirichlet boundary condition; Critical Sobolev exponent;

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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.

Last modified: 2019-04-28 14:10:01