Positive periodic solutions of second-order difference equations with weak singularities

Positive periodic solutions of second-order differential equations with weak singularities

where a, c : Z ® R+ are T-periodic functions, f Î C(Z × (0, ∞), R) is T-periodic with respect to t and singular at u = 0. Positive periodic solutions of second-order difference equations have been studied by many authors, see [1-6]. However, in these therein, the nonlinearities are nonsingular, what would happen if the nonlinearity term is singular? It is of interest to note here that singular ...

Periodic Solutions of Second Order Nonlinear Functional Difference Equations

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...

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...

Periodic solutions for nonlinear second-order difference equations

We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form y(t + 2) + by(t + 1) + cy(t) = f (y(t)), where c = 0 and f :R→ R is continuous. In our main result we assume that f exhibits sublinear growth and that there is a constant β > 0 such that u f (u) > 0 whenever |u| ≥ β. For such an equation we prove that ifN is an odd integer...

Nontrivial Periodic Solutions for Nonlinear Second-Order Difference Equations