GROUND STATE SIGN-CHANGING SOLUTION FOR SCHRODINGER-POISSON SYSTEM WITH STEEP POTENTIAL WELL

In the present paper, we investigate a class of nonlinear Schrodinger-Poisson system {-Delta u+ V-lambda(x)u + mu phi u = f (u) in R-3, -Delta phi = u(2) in R-3, where mu > 0 and V-lambda(x) = lambda V (x)+ 1 with lambda > 0. Under some mild assumptions on V and f, we prove the existence of ground state sign-changing solution for lambda > 0 large enough by adopting the deformation lemma and constrained minimization arguments. Then, the least energy of sign-changing solutions is strictly large than two times the ground state energy. Additionally, the phenomenon of concentration for ground state sign-changing solutions is also analysed as lambda -> infinity and mu -> 0.