On periodic solutions of nonlinear evolution equations in Banach spaces

摘要

We prove an existence result for T-periodic solutions to nonlinear evolution equations of the form (x)over dot(t) + A (t. x (t)) = f (t, x (t)), 0 < t < T. Here V hooked right arrow H hooked right arrow V* is an evolution triple, A: I x V --> V* is a uniformly monotone operator, and f : I x H --> V * is a Caratheodory mapping which is Holder continuous with respect to x in H and exponent 0 < alpha less than or equal to 1. For illustration, an example of a quasi-linear parabolic differential equation is worked out in detail. (C) 2002 Elsevier Science (USA). All rights reserved. [References: 10]