Sign-changing solutions for the Schr¨odinger-Poisson system with concave-convex nonlinearities in R³.

In this paper, we consider the following Schr¨odinger-Poisson system  -Δu + V(x)u + ϕu = |u|p-2u + λK(x)|u|q-2u in R3, -Δϕ = u2 in R3. Under the weakly coercive assumption on V and an appropriate condition on K, we investigate the cases when the nonlinearities are of concave-convex type, that is, 1 < q < 2 and 4 < p < 6. By constructing a nonempty closed subset of the sign-changing Nehari manifold, we establish the existence of least energy sign-changing solutions provided that λ ∈ (-∞, λ∗), where λ∗ > 0 is a constant. [ABSTRACT FROM AUTHOR]