Existence of Nontrivial Solutions for Perturbed Elliptic System in ℝ N

Abstract EN

We consider the perturbed nonlinear elliptic system - ε 2 Δ u + V ( x ) u = K ( x ) | u | 2 * - 2 u + H u ( u , v ) ,     x ∈ ℝ N , - ε 2 Δ v + V ( x ) v = K ( x ) | v | 2 * - 2 v + H v ( u , v ) ,     x ∈ ℝ N , where N ≥ 3 , 2 * = 2 N / ( N - 2 ) is the Sobolev critical exponent.

Under proper conditions on V , H , and K , the existence result and multiplicity of the system are obtained by using variational method provided ε is small enough.