On periodic solutions of nonlinear evolution equations in Banach spaces

Abstract

We prove an existence result for T-periodic solutions to nonlinear evolution equations of the form x(t)+A(t.x(t))=f(t.x(t)). O<t<T.

Here VHV* is an evolution triple, A :I×V→V* is a uniformly monotone operator, and f :I×H→V* is a Caratheodory mapping which is Hölder continuous with respect to x in H and exponent 0<1. For illustration, an example of a quasi-linear parabolic differential equation is worked out in detail.