| Texto completo | |
| Autor(es): |
Bonotto, E. M.
;
Federson, M.
;
Mesquita, C.
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | JOURNAL OF GEOMETRIC ANALYSIS; v. 33, n. 1, p. 37-pg., 2023-01-01. |
| Resumo | |
The aim of this paper is to investigate the existence and uniqueness of solutions of the following boundary value problem concerning generalized ODEs {dx/d tau = D[A(t)x + F(t)], integral(b)(a) d[K(s)] x(s) = r, for operators taking values in general Banach spaces. Up to now, this problemwas only tackled in the case of finite dimensional space-valued functions. We establish necessary and sufficient conditions not only for the existence of at least one solution, but also for the uniqueness of a solution. Another important result describes the solution in terms of a Green function and the fundamental operator of the corresponding homogeneous problem. We also explore the problem dx/d tau = D[A(t)x + F(t)] and we give necessary and sufficient conditions for the existence of a (theta, T)-periodic solution, where theta is an element of R, with. theta not equal 0, and T > 0, recalling that the notion of (theta, T)-periodic solution generalizes the notions of periodic, anti-periodic, almost periodic, and quasi-periodic solution. Examples are given to illustrate the main results. In addition, we apply the main theorems to abstract ODEs, as well as to a Volterra-Stieltjes-type integral equation, and we include examples of these as well. (AU) | |
| Processo FAPESP: | 20/14075-6 - Sistemas dinâmicos e seus atratores sob perturbação |
| Beneficiário: | Alexandre Nolasco de Carvalho |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |