Nontrivial solutions for a quasilinear elliptic system

Boundary value problems

Lu Yang¹  Xiyou Cheng¹ 

[1] School of Mathematics and Statistics, Lanzhou University, Lanzhou, P.R. China

关键词: elliptic equations;    Nehari manifold;    linking theorem;    minimax principle;   

DOI  :  10.1186/1687-2770-2014-34

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we deal with the existence of three nontrivial solutions for the potential system of p-Laplacian equations with homogeneous Dirichlet boundary conditions. Applying the Nehari procedure and abstract linking theorem on a product space, we give a linking structure for our variational problem, and then, combining with the classical minimax principle, we obtain three nontrivial critical values for the relevant energy functional. MSC:35J20, 35J25.

【 授权许可】

CC BY