Multiple positive almost periodic solutions for some nonlinear integral equations

Positive Almost Periodic Solutions for a Class of Nonlinear Duffing Equations with a Deviating Argument∗

In this paper, we study a class of nonlinear Duffing equations with a deviating argument and establish some sufficient conditions for the existence of positive almost periodic solutions of the equation. These conditions are new and complement to previously known results.

Dynamic Systems and Applications 17 (2008) 515-538 POSITIVE ALMOST AUTOMORPHIC SOLUTIONS FOR SOME NONLINEAR INFINITE DELAY INTEGRAL EQUATIONS

We state sufficient conditions for the existence of positive bounded, almost automorphic or almost periodic solutions of the following nonlinear infinite delay integral equation:

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

Ergodicity and Asymptotically Almost Periodic Solutions of Some Differential Equations

Using ergodicity of functions, we prove the existence and uniqueness of (asymptotically) almost periodic solution for some nonlinear differential equations. As a consequence, we generalize a Massera’s result. A counterexample is given to show that the ergodic condition cannot be dropped. 2000 Mathematics Subject Classification. Primary 34C27, 43A60, 37Axx, 28Dxx.

Existence of Solutions for some Nonlinear Volterra Integral Equations via Petryshyn's Fixed Point Theorem

In this paper, we study the existence of solutions of some nonlinear Volterra integral equations by using the techniques of measures of noncompactness and the Petryshyn's fixed point theorem in Banach space. We also present some examples of the integral equation to confirm the efficiency of our results.