Multi-bump Solutions for a Strongly Indefinite Semilinear Schrödinger Equation Without Symmetry or convexity Assumptions

Simple item page
dc.creatorChen, Shaowei
dc.date2008-05-18
dc.date.accessioned2026-07-07T09:39:38Z
dc.date.available2026-07-07T09:39:38Z
dc.descriptionIn this paper, we study the following semilinear Schrödinger equation with periodic coefficient: $$-\triangle u +V(x)u=f(x,u), u\in H^{1}(\mathbb{R}^{N}).$$ The functional corresponding to this equation possesses strongly indefinite structure. The nonlinear term $f(x,t)$ satisfies some superlinear growth conditions and need not be odd or increasing strictly in $t$. Using a new variational reduction method and a generalized Morse theory, we proved that this equation has infinitely many geometrically different solutions. Furthermore, if the solutions of this equation under some energy level are isolated, then we can show that this equation has infinitely many $m-$bump solutions for any positive integer $m\geq 2.$
dc.description37pages
dc.identifierhttps://arxiv.org/abs/0805.2711
dc.identifierhttp://arxiv.org/abs/0805.2711
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161244
dc.subjectAnalysis of PDEs
dc.subject35J20, 35J70
dc.titleMulti-bump Solutions for a Strongly Indefinite Semilinear Schrödinger Equation Without Symmetry or convexity Assumptions
dc.typetext

Files

Collections

arXiv