Asymptotic Behavior of Solutions of Delayed Difference Equations | Zendy

Josef Diblı́k | Zendy; Irena Hlavičková | Zendy

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Asymptotic Behavior of Solutions of Delayed Difference Equations

Author(s) -

Josef Diblı́k,

Irena Hlavičková

Publication year - 2011

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2011/671967

Subject(s) - mathematics , retract , integer (computer science) , class (philosophy) , type (biology) , domain (mathematical analysis) , graph , comparison theorem , mathematical analysis , pure mathematics , discrete mathematics , ecology , artificial intelligence , computer science , biology , programming language

This contribution is devoted to the investigation of the asymptotic behavior of delayed difference equations with an integer delay. We prove that under appropriate conditions there exists at least one solution with its graph staying in a prescribed domain. This is achieved by the application of a more general theorem which deals with systems of first-order difference equations. In the proof of this theorem we show that a good way is to connect two techniques—the so-called retract-type technique and Liapunov-type approach. In the end, we study a special class of delayed discrete equations and we show that there exists a positive and vanishing solution of such equations

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