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

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

Levitan Almost Periodic and Almost Automorphic Solutions of Second-order Monotone Differential Equations

The aim of this paper is the study of problem of existence of Levitan almost periodic, almost automorphic, recurrent and Poisson stable solutions of seconde order differential equation (1) x′′ = f(σ(t, y), x, x′), (y ∈ Y ) where Y is a complete metric space and (Y,R, σ) is a dynamical system (driving system). For equation (1) with increasing (with respect to second variable) function f the exis...

Almost-Periodic Weak Solutions of Second-Order Neutral Delay-Differential Equations with Piecewise Constant Argument

Differential equations with piecewise constant argument, which were firstly considered by Cooke and Wiener 1 , and Shah and Wiener 2 , usually describe hybrid dynamical systems a combination of continuous and discrete and so combine properties of both differential and difference equations. Over the years, great attention has been paid to the study of the existence of almost-periodic-type soluti...

Almost periodic solutions for a class of fourth-order nonlinear differential equations with a deviating argument

This work is concernedwith a class of fourth order semilinear ordinary differential equation with pseudo almost periodic environment and multiple delays. Specifically, we establish the existence and uniqueness of the pseudo almost periodic solutions. Furthermore, we discuss the global stability of the considered equation.

Perturbing Almost Periodic Differential Equations

ABSTRACT. When the zero solution of an almost periodic differential system is uniform-asymptotically stable, it is shown that the zero solution is diminishingly asymptotically stable and totally asymptotically stable. Generalization of the above theorem to bounded solutions and functional differential equations with finite time-lag are obtained by the same method. The techniques used in the pro...