Existence of Solutions for Schrodinger-Poisson Systems with Sign-Changing Weight

We study the existence of solutions for the Schrodinger-Poisson system {-Delta u+u+k(x)phi u = a(x) vertical bar u vertical bar(p-1), in R-3, -Delta phi = k(x)u(2,) in R-3, where 3 <= p<5, a(x) is a sign-changing function such that both the supports of a(+) and a(-) may have infinite measure. We show that the problem has at least one nontrivial solution under some assumptions.