Normalized ground state solutions for Kirchhoff type systems

Abstract

We consider the existence of ground state solutions for nonlinear Kirchhoff type systems in the whole space RN (2 ≤ N ≤ 4) with prescribed normalization. Two cases are studied: one is L2-supercritical and the other is mixed. In the first case, assuming that the coupling coefficient is big enough, we prove the existence of a ground state solution via minimax methods. In the second case, assuming that the coupling coefficient is sufficiently small, we show the existence of a local minimizer, which is, of course, also a ground state solution.