On qualitative and quantitative results for solutions to first-order dynamic equations on time scales
Carregando...
Data
2015-10-01
Autores
Domini dos Santos, Iguer Luis
Título da Revista
ISSN da Revista
Título de Volume
Editor
Springer
Resumo
In the present work, we study qualitative and quantitative results proposed in the paper Tisdell and Zaidi (Nonlinear Anal 68(11): 3504-3524, 2008) of first-order dynamic equations on time scales. Thus, we examine initial value problems described by dynamic equations on time scales of the form x(Delta) = f (t, x, x(sigma)). We obtain a result on the dependency of solutions to initial value problems with respect to initial values. Using Banach's fixed-point theorem, we prove the existence and uniqueness of solutions to initial value problems. On the other hand, under weaker hypothesis on f, using Schafer's fixed-point theorem, we obtain the existence of at least one solution to initial value problems.
Descrição
Palavras-chave
Dynamic equations, Existence of solutions, Continuous dependence, Time scales
Como citar
Boletin De La Sociedad Matematica Mexicana. Basel: Springer Basel Ag, v. 21, n. 2, p. 205-218, 2015.