Asymptotic expansion for nonlinear eigenvalue problems
| dc.creator | Aboud, Fatima | |
| dc.creator | Robert, Didier | |
| dc.date | 2009-03-05 | |
| dc.date.accessioned | 2026-07-07T12:49:15Z | |
| dc.date.available | 2026-07-07T12:49:15Z | |
| dc.description | In this paper we consider generalized eigenvalue problems for a family of operators with a quadratic dependence on a complex parameter. Our model is $L(λ)=-\triangle +(P(x)-λ)^2$ in $L^2(\R^d)$ where $P$ is a positive elliptic polynomial in $\R^d$ of degree $m\geq 2$. It is known that for $d$ even, or $d=1$, or $d=3$ and $m\geq 6$, there exist $λ\in\C$ and $u\in L^2(\R^d)$, $u\neq 0$, such that $L(λ)u=0$. In this paper, we give a method to prove existence of non trivial solutions for the equation $L(λ)u=0$, valid in every dimension. This is a partial answer to a conjecture in \cite{herowa}. | |
| dc.identifier | https://arxiv.org/abs/0903.0919 | |
| dc.identifier | http://arxiv.org/abs/0903.0919 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222338 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Functional Analysis | |
| dc.subject | Spectral Theory | |
| dc.title | Asymptotic expansion for nonlinear eigenvalue problems | |
| dc.type | text |