Existence of multiple periodic solutions for a semilinear evolution equation

Abstract

In this paper, we consider the existence of multiple periodic solutions for the problem \[ d u d t + L u = g ( u ) + h , t > 0 , u ( 0 ) = u ( T ) , \frac {{du}}{{dt}} + Lu = g(u) + h,t > 0,u(0) = u(T), \] where L L is a uniformly strongly elliptic operator with domain D ( L ) = H 0 m ( Ω ) , g : R → R D(L) = H_0^m(\Omega ),g:R \to R is a continuous mapping, T > 0 T > 0 and h : ( 0 , T ) → H 0 m ( Ω ) h:(0,T) \to H_0^m(\Omega ) is a measurable function.