EXISTENCE AND ASYMPTOTIC BEHAVIOR OF GROUND STATE SIGN-CHANGING SOLUTIONS FOR A NONLINEAR SCHRODINGER-POISSON-KIRCHHOFF SYSTEM IN R3

In this paper, we consider the existence and asymptotic behavior of ground state sign-changing solutions for the following nonlinear Schrodinger-Poisson-Kirchhoff system: {-(a+b integral(R3) vertical bar del u vertical bar(2) dx)Delta u + V(x)u +k(x)phi u = lambda f(x)u + g(x, u) in R-3, -Delta phi = k(x)u(2), in R-3, Under some mild assumptions, by using a series of constructive Nehari manifolds and a quantitative deformation lemma, we prove that the Schrodinger-Poisson-Kirchhoff system possesses at least one ground state sign-changing solution ub for all b > 0. Moreover, for any sequence {b(n)} -> 0(+) (n -> infinity), there exists a subsequence {b(nk)}, such that {u(bnk)} converges to u(0), where u(0) is a sign-changing solution of the equation -a Delta u + V(x)u = lambda f(x)u + g(x, u), x is an element of R-3.