Positive periodic solutions of functional differential equations

Positive periodic solutions of functional differential equations

We consider the existence, multiplicity and nonexistence of positive o-periodic solutions for the periodic equation x0ðtÞ 1⁄4 aðtÞgðxÞxðtÞ lbðtÞf ðxðt tðtÞÞÞ; where a; bACðR; 1⁄20;NÞÞ are o-periodic, Ro 0 aðtÞ dt40; Ro 0 bðtÞ dt40; f ; gACð1⁄20;NÞ; 1⁄20;NÞÞ; and f ðuÞ40 for u40; gðxÞ is bounded, tðtÞ is a continuous o-periodic function. Define f0 1⁄4 limu-0þ f ðuÞ u ; fN 1⁄4 limu-N f ðuÞ u ; i0...

Existence of Positive Periodic Solutions for Neutral Functional Differential Equations

We find sufficient conditions for the existence of positive periodic solutions of two kinds of neutral differential equations. Using Krasnoselskii’s fixed-point theorem in cones, we obtain results that extend and improve previous results. These results are useful mostly when applied to neutral equations with delay in bio-mathematics.

A note on positive periodic solutions of delayed differential equations

We consider the existence of positive ω-periodic solutions for the periodic equation x (t) = a(t)e x(t) x(t) − λb(t)f (x(t − τ (t))), where a, b ∈ C (R, [0, ∞)) are ω-periodic, ω 0 a(t)dt > 0, ω 0 b(t)dt > 0, f ∈ C ([0, ∞), [0, ∞)), and f (u) > 0 for u > 0, τ (t) is a continuous ω-periodic function.

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