Positive Periodic Solutions for Nonlinear Difference Equations with Periodic Coefficients

Eventually Periodic Solutions for Difference Equations with Periodic Coefficients and Nonlinear Control Functions

For nonlinear difference equations of the form xn F n, xn−1, . . . , xn−m , it is usually difficult to find periodic solutions. In this paper, we consider a class of difference equations of the form xn anxn−1 bnf xn−k , where {an}, {bn} are periodic sequences and f is a nonlinear filtering function, and show how periodic solutions can be constructed. Several examples are also included to illust...

Nonlinear Difference Equations with Periodic Solutions

For ten nonlinear difference equations with only p-periodic solutions it is shown that the characteristic polynomials of the corresponding linearized equations about the equilibria have only zeros which are p-th roots of unity. An analogous result is shown concerning two systems of such equations. Five counterexamples show that the reverse is not true. Some remarks are made concerning equations...

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...

Positive Solutions for Nonlinear Differential Equations with Periodic Boundary Condition

Existence of Periodic Positive Solutions for Abstract Difference Equations

has been considered. To the best of our knowledge, however, little has been done for the abstract difference equations see 7–9 . In this note, we will consider this problem. To this end, let X be a real Banach space and let K ⊂ X be a cone, then a Banach space X with a partial ordering ≤ induced by a coneK is called an ordered Banach space. On the other hand, we will denote the identity operato...