| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil
[2] Univ Sao Paulo, Dept Comp & Matemat, Fac Filosofia Ciencias & Letras Ribeirao Preto, BR-14040901 Ribeirao Preto, SP - Brazil
[3] Univ Fed Juiz de Fora, ICE, BR-36036900 Juiz De Fora, MG - Brazil
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | Mathematische Nachrichten; v. 288, n. 13, p. 1487-1511, SEP 2015. |
| Web of Science Citations: | 1 |
| Abstract | |
We consider measure functional differential equations (we write measure FDEs) of the form Dx = f (x(t), t) Dg, where f is Perron-Stieltjes integrable, xt is given by x(t) (theta) = x(t +theta),theta is an element of {[}-r, 0], with r > 0, and Dx and Dg are the distributional derivatives in the sense of the distribution of L. Schwartz, with respect to functions x :{[}t(0), infinity) -> R-n and g : {[}t(0), infinity) -> R, t(0) is an element of R, and we present new concepts of stability of the trivial solution, when it exists, of this equation. The new stability concepts generalize, for instance, the variational stability introduced by. S. Schwabik and M. Federson for FDEs and yet we are able to establish a Lyapunov-type theorem for measure FDEs via theory of generalized ordinary differential equations (also known as Kurzweil equations). (C) 2015 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim (AU) | |
| FAPESP's process: | 10/09139-3 - Non-absolute integration and differential equations |
| Grantee: | Márcia Cristina Anderson Braz Federson |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 09/06259-0 - Atractors for generalized ordinary differential equations and applications to functional differential equations |
| Grantee: | Eduard Toon |
| Support Opportunities: | Scholarships in Brazil - Doctorate |