Existence of Nontrivial Solutions for Perturbed Elliptic System in ℝN. (13th May 2014) - Jiang, Juan
Abstract : 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.