GROUND STATE SIGN-CHANGING SOLUTIONS FOR NONLINEAR SCHRODINGER-POISSON SYSTEM WITH INDEFINITE POTENTIALS

This paper is concerned with the following SchrodingerPoisson system { - Delta mu+V (x)u + K (x)phi u = a(x)vertical bar u vertical bar(p-2) in R3, -Delta phi= K(x)u(2) in R3, where 4 < p < 6. For the case that K is nonnegative, V and a are indefinite, we prove the above problem possesses one ground state sign-changing solution with exactly two nodal domains by constraint variational method and quantitative deformation lemma. Moreover, we show that the energy of sign-changing solutions is larger than that of the ground state solutions. The novelty of this paper is that the potential a is indefinite and allowed to vanish at infinity. In this sense, we complement the existing results obtained by Batista and Furtado [5].