Publicação: On qualitative and quantitative results for solutions to first-order dynamic equations on time scales
Data
2015-10-01
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Springer
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Acesso aberto
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.
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Inglês
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Boletin De La Sociedad Matematica Mexicana. Basel: Springer Basel Ag, v. 21, n. 2, p. 205-218, 2015.
