Periodic bifurcation from families of periodic solutions for(15)

Let A:D(A)\to E be an infinitesimal generator either of an analytic compact semigroup or of a contractive C_0-semigroup of linear operators acting in a Banach space E. In this paper we give both necessary and sufficient conditions for bifurcation of $T$-pe

Toseethis,observethatthefunctionuofLemma3.1satis esthefollowingintegralequation

t′u(t,ξ,ε)=AαeΛ(t s)fx(s,A αx(s,ξ,0))u(s,ξ,ε)ds+

0 to(x(s,ξ,ε) x(s,ξ,0))+AαeΛ(t s)

Φh,ε:E→Ebede nedby