Periodic trajectories for evolution equations in Banach spaces

Abstract

The existence of periodic solutions for the evolution equation $$ y'(t)+Ay(t) i F(t,y(t)) $$ 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.

Keywords

• Periodic solution
• evolution equation of parabolic type.