(untitled) (Journal of Partial Differential Equations, 2011)
We study the existence of solutions for the Schrödinger-Poisson system -Δu+u+k(x)φu=α(x)|u|^p-1u, in R^3, -Δφ=k(x)u^2, in R^3, where 3 ≤ p < 5, α(x) is a sign-changing function such that both the supports of α^+ and α^- may have infinite measure. We show that the problem has at least one nontrivial solution under some assumptions.