Periodic bifurcation from families of periodic solutions for semilinear differential equations with Lipschitzian perturbations in Banach spaces
| dc.creator | Kamenskii, Mikhail | |
| dc.creator | Makarenkov, Oleg | |
| dc.creator | Nistri, Paolo | |
| dc.date | 2007-09-28 | |
| dc.date.accessioned | 2026-07-07T08:32:57Z | |
| dc.date.available | 2026-07-07T08:32:57Z | |
| dc.description | Let A:D(A)\to E be an infinitesimal generator either of an analytic compact semigroup or of a contractive C_0-semigroup of linear operators acting in a Banach space E. In this paper we give both necessary and sufficient conditions for bifurcation of $T$-periodic solutions for the equation x'=Ax+f(t,x)+e g(t,x,e) from a k-parameterized family of T-periodic solutions of the unperturbed equation corresponding to e=0. We show that by means of a suitable modification of the classical Mel'nikov approach we can construct a bifurcation function and to formulate the conditions for the existence of bifurcation in terms of the topological index of the bifurcation function. To do this, since the perturbation term g is only Lipschitzian we need to extend the classical Lyapunov-Schmidt reduction to the present nonsmooth case. | |
| dc.description | Submitted to Adv. Nonlinear Stud | |
| dc.identifier | https://arxiv.org/abs/0709.4679 | |
| dc.identifier | http://arxiv.org/abs/0709.4679 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138963 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 34G05; 37G15; 47D05 | |
| dc.title | Periodic bifurcation from families of periodic solutions for semilinear differential equations with Lipschitzian perturbations in Banach spaces | |
| dc.type | text |