Multiple bound states for the Schrödinger-Poisson problem

Abstract

In this paper, we study the problem { -Δu + u + V(x)u = u p, -Δ V = λu2, lim |x| → + ∞ V(x)=0, where u, V : ℝ3 → ℝ are radial functions, λ > 0 and 1 < p < 5. We give multiplicity results, depending on p and on the parameter λ. © 2008 World Scientific Publishing Company.