Existence and Nonexistence of Positive Solutions of Indefinite Elliptic Problems in $\rz^N$

dc.creatorSchneider, Matthias
dc.date2002-06-07
dc.date.accessioned2026-07-07T04:48:57Z
dc.date.available2026-07-07T04:48:57Z
dc.descriptionOur purpose is to find positive solutions $u \in D^{1,2}(\rz^N)$ of the semilinear elliptic problem $-\laplace u - λV(x) u = h(x) u^{p-1}$ for $2<p$. The functions $V$ and $h$ may have an indefinite sign and the linearized operator need not to have a first (principal) eigenvalue, e.g. we allow $V\equiv 1$. We give precise existence and nonexistence criteria, which depend on $λ$ and on the growth of $h^{-}$ and $h^{+}/V^+$. Existence theorems are obtained by constrained minimization. The mountain pass theorem leads to a second solution.
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/math/0206070
dc.identifierhttp://arxiv.org/abs/math/0206070
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64248
dc.subjectAnalysis of PDEs
dc.subjectFunctional Analysis
dc.subject35J65, 35D05
dc.titleExistence and Nonexistence of Positive Solutions of Indefinite Elliptic Problems in $\rz^N$
dc.typetext

Files

Collections