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

By(3.6)and(3.5)thereexistsM>0suchthatthelastinequalitycanberewrittenas

u(t,ξ1,ε) u(t,ξ2,ε) u(s,ξ1,ε) u(s,ξ2,ε)

(t s)α