Ground state solutions of Nehari-Pohozaev type for Kirchhoff-type problems with general potentials

This paper is dedicated to studying the following Kirchhoff-type problem { - (a + b integral(R3) |del u|(2)dx) Delta u + V(x) u = f (u), x is an element of R-3; u is an element of H-1(R-3), where a > 0, b >= 0 are two constants, V(x) is differentiable and f is an element of C(R, R). By introducing some new tricks, we prove that the above problem admits a ground state solution of Nehari- Pohozaev type and a least energy solution under some mild assumptions on V and f. Our results generalize and improve the ones in Guo (J Differ Equ 259: 2884- 2902, 2015) and Li and Ye (J Differ Equ 257: 566- 600, 2014) and some other related literature.