The geometry of the critical set of nonlinear periodic Sturm-Liouville operators
| dc.creator | Burghelea, Dan | |
| dc.creator | Saldanha, Nicolau C. | |
| dc.creator | Tomei, Carlos | |
| dc.date | 2007-07-09 | |
| dc.date | 2008-10-17 | |
| dc.date.accessioned | 2026-07-07T12:51:43Z | |
| dc.date.available | 2026-07-07T12:51:43Z | |
| dc.description | We study the critical set C of the nonlinear differential operator F(u) = -u" + f(u) defined on a Sobolev space of periodic functions H^p(S^1), p >= 1. Let R^2_{xy} \subset R^3 be the plane z = 0 and, for n > 0, let cone_n be the cone x^2 + y^2 = tan^2 z, |z - 2 pi n| < pi/2; also set Sigma = R^2_{xy} U U_{n > 0} cone_n. For a generic smooth nonlinearity f: R -> R with surjective derivative, we show that there is a diffeomorphism between the pairs (H^p(S^1), C) and (R^3, Sigma) x H where H is a real separable infinite dimensional Hilbert space. | |
| dc.description | Added references, fixed typos; 24 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0707.1256 | |
| dc.identifier | http://arxiv.org/abs/0707.1256 | |
| dc.identifier | J. Differential Equations246(2009) 3380-3397 | |
| dc.identifier | doi:10.1016/j.jde.2008.10.021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223083 | |
| dc.subject | Functional Analysis | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 34B15; 34B24; 46T05 | |
| dc.title | The geometry of the critical set of nonlinear periodic Sturm-Liouville operators | |
| dc.type | text |