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

Author

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  • Gabor, Grzegorz
  • Ruszkowski, Sebastian
  • Vítovec, Jiří

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.

Suggested Citation

  • Gabor, Grzegorz & Ruszkowski, Sebastian & Vítovec, Jiří, 2015. "Ważewski type theorem for non-autonomous systems of equations with a disconnected set of egress points," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 358-369.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:358-369
    DOI: 10.1016/j.amc.2015.05.027
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    Cited by:

    1. Baštinec, J. & Diblík, J. & Pinelas, S. & Vala, J., 2022. "Determining the initial data generating solutions with prescribed behaviour of a triangular system of linear discrete equations," Applied Mathematics and Computation, Elsevier, vol. 425(C).

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