Ground states and geometrically distinct solutions for periodic Choquard-Pekar equations
type: Item
instance of: scholarly article
title: Ground states and geometrically distinct solutions for periodic Choquard-Pekar equations
zbMATH Open document ID: 1456.35187
author: Dongdong Qin
author: Vicenţiu D. Rădulescu
author: Xianhua X. H. Tang
published in: Journal of Differential Equations
publication date: 2021-01-08T00:00:00Z
review text: The authors study the non-autonomous Choquard-Pekar equation: \[-\vartriangle u + V(x)u = (W *F(u))f(u), \quad x \in \mathbb R^N (N \geq 2), \; u \in H^1(\mathbb R^N),\] where the potential \(V(x)\) is 1-periodic and 0 lies in a gap of the spectrum of the Schrödinger operator \(- \vartriangle + \, V\). Under some general assumptions concerning the potential \(W\) and the nonlinearity \(f\), they prove the existence of ground state solutions. They also construct infinitely many geometrically distinct solutions by using variational methods and deformation arguments.
reviewed by: Anthony D. Osborne
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 46N50
zbMATH DE Number: 7291353
zbMATH Keywords: Choquard-Pekar equation
zbMATH Keywords: ground state solution
zbMATH Keywords: strongly indefinite problem
zbMATH Keywords: geometrically distinct solutions
MaRDI profile type: Publication
full work available at URL: j.jde.2020.11.021
OpenAlex ID: W3098932406
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DOI: 10.1016/J.JDE.2020.11.021
description: scientific article; zbMATH DE number 7291353