Existence of a ground-state solution for a quasilinear Schrödinger system - Zhang, Xue; Zhang, Jing (Frontiers in Physics, 2024)
In this paper, we consider the following quasilinear Schrödinger system { arraylc -Δ u+ u+k2[Δ |u|^2]u=2αα+β|u|^α-2u|v|^β, & x R^N, -Δ v+ v+k2[Δ|v|^2]v=2βα+β|u|^α|v|^β-2v, & x R^N, array . where k<0 is a real constant, α >1, β >1, α+β<2^*. We take advantage of the critical point theorem developed by Jeanjean J, combine with Pohožaev identity to obtain the existence of a ground state solution, which is the nontrivial solution with least possible energy.