On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions

Resonance in Undamped Second-order Nonlinear Equations with Periodic Forcing

where g and p are real valued functions continuous on the reals R , p(t+2n) = p(t), and the solutions of (1) are uniquely determined by their initial conditions. If g is nonlinear, the question of whether all solutions of (1) are bounded on R has long been recognized as nontrivial and challenging. For the special case of g(x) = 2x Morris [1] was able to show that this question has an affirmativ...

Periodic solutions for a second order nonlinear functional differential equation

The second order nonlinear delay differential equation with periodic coefficients x ′′(t)+ p(t)x ′(t)+ q(t)x(t) = r(t)x ′(t − τ(t))+ f (t, x(t), x(t − τ(t))), t ∈ R is considered in this work. By using Krasnoselskii’s fixed point theorem and the contraction mapping principle, we establish some criteria for the existence and uniqueness of periodic solutions to the delay differential equation. c ...

Almost Periodic Solutions of Second Order Nonlinear Differential Equations with Almost Periodic Forcing

Positive solutions of nonlinear second-order periodic boundary value problems

Ruyun Ma, Chenghua Gao, and Ruipeng Chen Department of Mathematics, Northwest Normal University, Lanzhou 730070, China Correspondence should be addressed to Ruyun Ma, ruyun [email protected] Received 31 August 2010; Revised 30 October 2010; Accepted 8 November 2010 Academic Editor: Irena Rachůnková Copyright q 2010 Ruyun Ma et al. This is an open access article distributed under the Creative Commons A...

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...