Results on infinite dimensional topology and applications to the structure of the critical set of nonlinear Sturm-Liouville operators
| dc.creator | Burghelea, Dan | |
| dc.creator | Saldanha, Nicolau C. | |
| dc.creator | Tomei, Carlos | |
| dc.date | 2001-07-27 | |
| dc.date | 2001-10-17 | |
| dc.date.accessioned | 2026-07-07T04:42:45Z | |
| dc.date.available | 2026-07-07T04:42:45Z | |
| dc.description | We consider the nonlinear Sturm-Liouville differential operator $F(u) = -u'' + f(u)$ for $u \in H^2_D([0, π])$, a Sobolev space of functions satisfying Dirichlet boundary conditions. For a generic nonlinearity $f: \RR \to \RR$ we show that there is a diffeomorphism in the domain of $F$ converting the critical set $C$ of $F$ into a union of isolated parallel hyperplanes. For the proof, we show that the homotopy groups of connected components of $C$ are trivial and prove results which permit to replace homotopy equivalences of systems of infinite dimensional Hilbert manifolds by diffeomorphisms. | |
| dc.description | 23 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/math/0107197 | |
| dc.identifier | http://arxiv.org/abs/math/0107197 | |
| dc.identifier | J. Differential Equations 188 (2003) 569-590 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61915 | |
| dc.subject | Functional Analysis | |
| dc.subject | Primary 34L30, 58B05, Secondary 34B15, 46T05 | |
| dc.title | Results on infinite dimensional topology and applications to the structure of the critical set of nonlinear Sturm-Liouville operators | |
| dc.type | text |