Sign-changing solutions to critical Schrödinger equation with Hartree-type nonlinearity.

In this paper, we are interested in the following Schrödinger equation - Δ u + λ V (x) u = (I α ∗ | u | p ) | u | p - 2 u + | u | 4 u in R 3 , where λ is a positive parameter, V ∈ C (R , R +) and α ∈ (0 , 3) , p ∈ (2 + α , 3 + α) . Under some reasonable conditions on potential function V, particularly V allows to have nonisolated zero, we first establish the existence of positive ground-state solution and the corresponding energy estimates based on Nehari manifold. Subsequently, with the help of quantitative deformation lemma and invariant sets of descending flow, we also obtain the existence of ground-state sign-changing solution by adopting constrained minimization arguments on the sign-changing Nehari manifold. In this process, a new existence result of zero, which can be regarded as a generalization of Miranda's theorem, plays an essential role. Besides, the asymptotic behavior of sign-changing solutions is also studied when λ tends to infinity. [ABSTRACT FROM AUTHOR]