Existence and concentration of ground state solution to a nonlocal Schrödinger equation

We study a class of Schrodinger–Kirchhoff system involving a critical exponent. We aim to find suitable conditions to assure the existence of a positive ground state solution of Nehari–Pohozaev type ue with exponential decay at infinity for e, and ue concentrates around a global minimum point of V as e → 0+. The nonlinear term includes the nonlinearity f(u) ∼ |u|p−1u for the well-studied case p ∈ [3, 5) and the less-studied case p ∈ (2, 3).