Asymptotic behavior of solutions of systems of dynamic equations on time scales in a set whose boundary is a combination of strict egress and strict ingress points

Asymptotic behavior of solutions of systems of dynamic equations on time scales in a set whose boundary is a combination of strict egress and strict ingress points

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Article ID: iaor20142056
Volume: 238
Start Page Number: 289
End Page Number: 299
Publication Date: Jul 2014
Journal: Applied Mathematics and Computation
Authors: ,
Keywords: programming: nonlinear, programming: dynamic, differential equations
Abstract:

In this paper we study the asymptotic behavior of solutions of nonlinear dynamic systems on time scales of the form y Δ ( t ) = f ( t , y ( t ) ) , equ1 where f :T × R n R n equ2 and T equ3 is a time scale. For a given set Ω T × R n equ4, we formulate the conditions for function f, which guarantee that at least one solution y of the above system stays in Ω equ5. The dimension of the space of initial data generating such solutions is discussed and perturbed linear systems are considered as well. A linear system with singularity at infinity is considered as an example.

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