On semiclassical ground states for Hamiltonian elliptic system with critical growth - Zhang, Jian; Tang, Xianhua; Zhang, Wen (Topological Methods in Nonlinear Analysis, 2016)
In this paper, we study the following Hamiltonian elliptic system with gradient term and critical growth: equation* cases -ε^2Δ ψ +ε b· abla ψ +ψ=K(x)f(|η|)φ+W(x)|η|^2^*-2φ &in R^N, -ε^2Δ φ -ε b· abla φ +φ=K(x)f(|η|)ψ+W(x)|η|^2^*-2ψ &in R^N, cases equation* where η=(ψ,φ)R^N→R^2, K, WC(R^N, R), ε is a small positive parameter and b is a constant vector. We require that the nonlinear potentials K and W have at least one global maximum. Combining this with other suitable assumptions on f, we prove the existence, exponential decay and concentration phenomena of semiclassical ground state solutions for all sufficiently small ε> 0