Periodic bifurcation from families of periodic solutions for(17)

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

Sincethefamily h∈VBRk(h,r(h))coverstheset

V.

Byassumption

3

thereisL>0suchthat (

1′Pξ(h1,0)

Finallythecontinuityassumptions1,2and3implythatξsatis es(5.2)andd′). (h1,ξ(h1,ε1),ε2) Q (h1,ξ(h1,ε1),ε1) .Q References

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Sadovskii,Measuresofnoncompactnessandcondensingoperators.Translatedfromthe1986RussianoriginalbyA.Iacob.OperatorTheory:AdvancesandApplications,55.BirkhauserVerlag,Basel,1992.

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equations,NonlinearAnal.56(2004),1011–1046.

[3]A.Buica,J.LlibreandO.Makarenkov,Lyapunov–Schmidtreductionfornon-

smoothfunctionswithapplicationtoMalkin’sproblemontheexistenceofpe-riodicsolutions,inprogress.

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derMathematischenWissenschaften,251,Springer-Verlag,NewYork-Berlin,1982.

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