Positive ground states for nonlinear Schrodlinger-Kirchhoff equations with periodic potential or potential well in R-3

This work is devoted to the nonlinear Schrodinger-Kirchhoff-type equation -(a+b integral(R3) vertical bar del vertical bar(2) dx) Delta u + V(x)u = f(x,u), in R-3, where a > 0, b >= 0, the nonlinearity f(x,.) is 3-superlinear and the potential V is either periodic or exhibits a finite potential well. By the mountain pass theorem, Lions' concentration-compactness principle, and the energy comparison argument, we obtain the existence of positive ground state for this problem without proving the Palais-Smale compactness condition.