Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 103, pp. 1-8.
Title: Periodic trajectories for evolution equations in Banach spaces
Author: Mircea D. Voisei (Univ. of Texas, Edinburg, TX, USA)
Abstract:
The existence of periodic solutions for the evolution
equation
$$
y'(t)+Ay(t)\ni F(t,y(t))
$$
is investigated under considerably simple assumptions on
$A$ and $F$. Here $X$ is a Banach space, the operator
$A$ is $m$-accretive, $-A$ generates a compact semigroup,
and $F$ is a Caratheodory mapping. Two examples
concerning nonlinear parabolic equations are presented.
Submitted August 3, 2005. Published September 28, 2005.
Math Subject Classifications: 47J35, 34C25, 35K55.
Key Words: Periodic solution, evolution equation of parabolic type.