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

Sahand Communications in Mathematical Analysis

Somayeh Khademloo¹  Saeed Khanjany Ghazi¹ 

[1] Department of Basic Sciences, Babol Noushirvani University of Technology, 47148-71167, Babol, Iran.;

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

DOI  :  10.22130/scma.2018.46462.98

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown