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

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We study a class of Schrödinger–Kirchhoff system involving a critical exponent. We aim to find suitable conditions to assure the existence of a positive ground state solution of Nehari–Pohoz̆aev type uε with exponential decay at infinity for ε, and uε concentrates around a global minimum point of V as ε → 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).