Positive Periodic Solutions of Nonlinear First-Order Functional Difference Equations

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Positive Periodic Solutions of Nonlinear First-Order Functional Difference Equations

Ruyun Ma, Tianlan Chen, and Yanqiong Lu Department of Mathematics, Northwest Normal University, Lanzhou 730070, China Correspondence should be addressed to Ruyun Ma, ruyun [email protected] Received 12 October 2010; Accepted 19 December 2010 Academic Editor: Marko Robnik Copyright q 2010 Ruyun Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which pe...

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We obtain the existence and multiplicity of positive T -periodic solutions for the difference equations ∆x(n) = a(n, x(n))− λb(n)f(x(n− τ(n))) and ∆x(n) + a(n, x(n)) = λb(n)f(x(n− τ(n))), where f(·) may be singular at x = 0. Using a fixed point theorem in cones, we extend recent results in the literature.

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The development of the study of periodic solution of functional difference equations is relatively rapid. There has been many approaches to study periodic solutions of difference equations, such as critical point theory, fixed point theorems in Banach spaces or in cones of Banach spaces, coincidence degree theory, KaplanYorke method, and so on, one may see [3-7,11,13-15] and the references ther...

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ژورنال

عنوان ژورنال: Discrete Dynamics in Nature and Society

سال: 2010

ISSN: 1026-0226,1607-887X

DOI: 10.1155/2010/419536