A nonlinear eigenvalue problem in R and multiple solutions of nonlinear Schrödinger equation
Advances in Differential Equations
| dc.creator | Felmer, P. | |
| dc.creator | Torres, J. | |
| dc.date | 2020-08-14T20:43:10Z | |
| dc.date | 2022-07-08T20:16:49Z | |
| dc.date | 2020-08-14T20:43:10Z | |
| dc.date | 2022-07-08T20:16:49Z | |
| dc.date | 2002 | |
| dc.date.accessioned | 2023-08-22T04:14:11Z | |
| dc.date.available | 2023-08-22T04:14:11Z | |
| dc.identifier | 15000001 | |
| dc.identifier | 15000001 | |
| dc.identifier | https://hdl.handle.net/10533/245981 | |
| dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/8318684 | |
| dc.description | Consider the nonlinear Sturm-Liouville eigenvalue problem u′′−Q(x)ulim|x|→∞u(x)+λ(Mu+f(u))=0,x∈R,=lim|x|→∞u′(x)=0,u″−Q(x)u+λ(Mu+f(u))=0,x∈R,lim|x|→∞u(x)=lim|x|→∞u′(x)=0, where the potential QQ is positive and coercive, the function f(s)f(s) behaves like spsp, p>1p>1, MM is a positive constant and λλ is a positive parameter. When the domain is a bounded interval, Rabinowitz global bifurcation theory applies to this problem, showing the existence of unbounded branches of nontrivial solutions. Even more, Rabinowitz proved that the branches bend back. This last fact has as a consequence a multiplicity result for solutions of a related nonlinear Schr\"odinger equation. In this paper we prove that this result holds true when the domain is RR. The main point of the article is the proof that the branches bend back, the place where the noncompactness of RR poses a difficulty. | |
| dc.description | CMM | |
| dc.description | FONDAP | |
| dc.description | FONDAP | |
| dc.language | eng | |
| dc.relation | instname: ANID | |
| dc.relation | reponame: Repositorio Digital RI2.0 | |
| dc.relation | https://projecteuclid.org/euclid.ade/1356651635 | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.title | A nonlinear eigenvalue problem in R and multiple solutions of nonlinear Schrödinger equation | |
| dc.title | Advances in Differential Equations | |
| dc.type | Articulo | |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion |