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Open Access Research

Nontrivial solutions for a quasilinear elliptic system

Xiyou Cheng* and Lu Yang

Author Affiliations

School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, P.R. China

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Boundary Value Problems 2014, 2014:34  doi:10.1186/1687-2770-2014-34

Published: 7 February 2014

Abstract

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.

Keywords:
elliptic equations; Nehari manifold; linking theorem; minimax principle