Ważewski type theorem for non-autonomous systems of equations with a disconnected set of egress points

Grzegorz Gabor, Sebastian Ruszkowski and Jiří Vítovec

Applied Mathematics and Computation, 2015, vol. 265, issue C, 358-369

Abstract: In this paper we study an asymptotic behavior of solutions of nonlinear dynamic systems on time scales of the form yΔ(t)=f(t,y(t)),where f:T×Rn→Rn, and T is a time scale. For a given set Ω⊂T×Rn, we formulate conditions for function f which guarantee that at least one solution y of the above system stays in Ω. Unlike previous papers the set Ω is considered in more general form, i.e., the time section Ωt is an arbitrary closed bounded set homeomorphic to the disk (for every t∈T) and the boundary ∂TΩ does not contain only egress points. Thanks to this, we can investigate a substantially wider range of equations with various types of bounded solutions. A relevant example is considered.

Keywords: Time scale; Dynamic system; Non-autonomous system; Difference equation; Asymptotic behavior of solution; Retract method (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:265:y:2015:i:c:p:358-369

DOI: 10.1016/j.amc.2015.05.027

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