Existence and Nonexistence of Positive Solutions of Indefinite Elliptic Problems in $\rz^N$
| dc.creator | Schneider, Matthias | |
| dc.date | 2002-06-07 | |
| dc.date.accessioned | 2026-07-07T04:48:57Z | |
| dc.date.available | 2026-07-07T04:48:57Z | |
| dc.description | Our 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.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/math/0206070 | |
| dc.identifier | http://arxiv.org/abs/math/0206070 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64248 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Functional Analysis | |
| dc.subject | 35J65, 35D05 | |
| dc.title | Existence and Nonexistence of Positive Solutions of Indefinite Elliptic Problems in $\rz^N$ | |
| dc.type | text |