Existence of Ground States for Kirchhoff-Type Problems with General Potentials

In this paper, we consider 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, b > 0, V is an element of C(R-3, R) and f is an element of C( R, R). Using variational method and some new analytical techniques, we show the existence of ground state solutions for the above problem. Assumptions imposed on the potential V and the nonlinearity f are general, and they are satisfied by several functions. Our results generalize and improve the ones obtained recently in [Li and Ye, J. Differential Equations (2014)], [Tang and Chen, Calc. Var. PartialDifferential Equations (2017)], [Guo, J. Differential Equations (2015)] and some other related literature.