Abstract
AbstractWe study a system of equations known as Schrödinger–Poisson problem proving that the set of sign-changing solutions has a rich structure in the semiclassical limit. Indeed we construct non-radial multi-peak solutions with an arbitrary large number of positive and negative peaks which are displaced in suitable symmetric configurations and which collapse to the same point as ϵ ⟶ 0. The proof is based on the Lyapunov–Schmidt reduction.KeywordsSchrödinger–Poisson problemsemiclassical limitcluster solutionssign-changing solutionsvariational methodsLyapunov–Schmidt reduction
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