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: 2018-11-01
Authors : Somayeh Khademloo; Saeed Khanjany Ghazi;
Page : 39-57
Keywords : Variational methods; Nehari manifold; Dirichlet boundary condition; Critical Sobolev exponent;
Abstract
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.
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Last modified: 2019-04-28 14:10:01