Ground states for Schrödinger-Poisson type systems

In this paper we consider the following elliptic system in, where λ is a real parameter, p ∈(1, 5) if λ < 0 while p ∈(3, 5) if λ > 0 and K(x), a(x) are non-negative real functions defined on ℝ3. Assuming that limpipexpipe→+∞K(x)=K∞ >0 and limpipexpipe→+∞a(x)=a∞ >0 and satisfying suitable assumptions, but not requiring any symmetry property on them, we prove the existence of positive ground states, namely the existence of positive solutions with minimal energy. © 2011 Università degli Studi di Napoli "Federico II".