The topology of critical sets of some ordinary differential operators
| dc.creator | Saldanha, Nicolau C. | |
| dc.creator | Tomei, Carlos | |
| dc.date | 2005-01-05 | |
| dc.date.accessioned | 2026-07-07T05:15:51Z | |
| dc.date.available | 2026-07-07T05:15:51Z | |
| dc.description | We survey recent work of Burghelea, Malta and both authors on the topology of critical sets of nonlinear ordinary differential operators. For a generic nonlinearity $f$, the critical set of the first order nonlinear operator $F_1(u)(t) = u'(t) + f(u(t))$ acting on the Sobolev space $H^1_p$ of periodic functions is either empty or ambient diffeomorphic to a hyperplane. For the second order operator $F_2(u)(t) = -u''(t) + f(u(t))$ on $H^2_D$ (Dirichlet boundary conditions), the critical set is ambient diffeomorphic to a union of isolated parallel hyperplanes. For second order operators on $H^2_p$, the critical set is not a Hilbert manifold but is still contractible and admits a normal form. The third order case is topologically far more complicated. | |
| dc.description | 15 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/math/0501071 | |
| dc.identifier | http://arxiv.org/abs/math/0501071 | |
| dc.identifier | Progress in Nonlinear Differential Equations and Their Applications, Vol. 66, 491-504, 2005. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73774 | |
| dc.subject | Functional Analysis | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 34L30; 58B05; 34B15; 46T05 | |
| dc.title | The topology of critical sets of some ordinary differential operators | |
| dc.type | text |