Multiplicity of solutions for a noncooperative [formula omitted]-Laplacian elliptic system in [formula omitted

Abstract

In this paper, we study a system of p-Laplacian elliptic equations Δ p u - | u | p - 2 u = F u ( | x | , u , v ) in R N , - Δ p v + | v | p - 2 v = F v ( | x | , u , v ) in R N , u , v ∈ W 1 , p ( R N ) . Applying Principle of Symmetric Criticality and a Limit Index Theory, under some assumptions on F u , F v , we can obtain the existence of infinitely many radial solutions and nonradial solutions for the above system, which extends some results in Li (Nonlinear Anal. TMA 25 (1995) 1371).