Almost Periodic Solutions of Periodic Linear Partial Functional Differential Equations

Almost periodic linear differential equations with non-separated solutions

A celebrated result by Favard states that, for certain almost periodic linear differential systems, the existence of a bounded solution implies the existence of an almost periodic solution. A key assumption in this result is the separation among bounded solutions. Here we prove a theorem of anti-Favard type: if there are bounded solutions which are non-separated (in a strong sense) sometimes al...

Weighted Pseudo Almost Periodic Solutions for Functional Differential Equations

By means of the exponential dichotomy method and the properties of the weighted pseudo almost periodic functions, sufficient conditions are obtained for the existence of weighted pseudo almost periodic solutions of functional differential equations with finite delay.

Periodic Solutions of Nonlinear Partial Differential Equations

As the existence theory for solutions of nonlinear partial differential equations becomes better understood, one can begin to ask more detailed questions about the behavior of solutions of such equations. Given the bewildering complexity which can arise from relatively simple systems of ordinary differential equations, it is hopeless to try to describe fully the behavior which might arise from ...

Periodic Solutions of Chaotic Partial Differential Equations

Almost Periodic Mild Solutions of a Class of Partial Functional Differential Equations

We study the existence of almost periodic mild solutions of a class of partial functional differential equations via semilinear almost periodic abstract functional differential equations of the form (∗) x′ = f(t, x, xt) . To this end, we first associate with every almost periodic semilinear equation (∗∗) x′ = F (t, x) a nonlinear semigroup in the space of almost periodic functions. We then give...