Periodic solutions for evolution inclusions with time-dependent subdifferentials

• Autorzy: Matzakos N. , Papageorgiu N. S.
• Języki publikacji: EN

Abstrakty

EN

In this paper we examine a periodic evolution equation driven by a time-dependent subdifferential and with a multivalued forcing term. Using a fixed point theorem for pseudo-acyclic multifunctions we prove the existence of periodic trajectories. This approach requires a study of the structure of the solution set of the Cauchy problem, which is also conducted in this paper.

Słowa kluczowe

EN

evolution equation; periodic solution; subdifferential; fixed point; parabolic equations

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 3
• Strony: 521--538
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Matzakos N.

• National Technical University, Department of Mathematics, Zografou Campus, Athens 157 80, Greece

autor

Papageorgiu N. S.

• National Technical University, Department of Mathematics, Zografou Campus, Athens 157 80, Greece

Bibliografia

• [1] V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff International Publishing, Leyden, The Netherlands (1976).
• [2] R. Becker, Periodic solutions of semilinear equations of evolution of compact type, J. Math, Anal. Appi. 82 (1981), 33-48.
• [3] H. Brezis, Operateurs Maximaux Monotones, North Holland, Amsterdam 1973.
• [4] F. Βrowder, Existence of periodic solutions for nonlinear equations of evolution, Proc. Nat. Acad. Sci. USA 53 (1965), 1110-1113.
• [5] B. Cornet, Existence of slow solutions for a class of differential inclusions, J. Math. Anal. Appl. 96 (1983), 130-147.
• [6] C. Henry, Differential equations with discontinuous right hand side for planning procedures, J. Economic Theory 4 (1972), 545-551.
• [7] N. Hirano, Existence of periodic solutions for nonlinear evolution equations in Hilbert spaces, Proc. AMS 120 (1994), 185-192.
• [8] S. Hu, N. S. Papageorgiou, On the existence of periodic solutions for a class of nonlinear evolution inclusions, Bollettino UMI 7 (1993), 591-605.
• [9] S. Hu, N. S. Papageorgiou, Time-Dependent Subdifferential Evolution Inclusions and Optimal Control, Memoirs of the AMS, Vol. 133, No 632, Providence, R.I (1998).
• [10] S. Hu, N. S. Papageorgiou, Handbook of Multivalued Analysis. Volume I: Theory, Kluwer, Dordrecht, The Netherlands (1997).
• [11] D. M. Hyman, On decreasing sequences of compact absolute retracts, Fund. Math. 64 (1969), 91-97.
• [12] N. Kenmochi, Some nonlinear parabolic variational inequalities, Israel J. Math 22 (1975), 304-330.
• [13] M. A. Krasnoselskii, Α. V. Pokrovskii, Systems with Hystertsis, Springer, Berlin [14] (1988).
• [14] J.-M. Lasry, R. Robert, Degré topologique pour certains couples des fonctions et applications aux équations différentielles multivoques, CRAS Paris 2 8 3 (1976), 163-166.
• [15] J.-J. Moreau, Evolution problem associated with a moving convex set in a Hilbert space, J. Diff. Eqns. 26 (1977), 347-374.
• [16] Ν. S. Papageorgiou, On parametric evolution inclusions of the subdifferential type with applications to optimal control problems, Trans. AMS 347 (1995), 203-231.
• [17] Ν. S. Papageorgiou, Ν. Shahzad, Propereties of the solution set of nonlinear evolution inclusions, Appi. Math. Optim. 36 (1997), 1-20.
• [18] N. S. Papageorgiou, N. Yannakakis, Extremal solutions and strong relaxation for nonlinear periodic evolution inclusions, Proc. Edinburgh Math. Soc. 43 (2000), 1-18.
• [19] J. Prüss, Periodic solutions of semilinear evolution equations, Nonlin. Anal. 3 (1979), 601-612.
• [20] R. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equation, Math. Surveys and Monographs, 49, AMS, Providence R.I. (1997).
• [21] I. Vrabie, Periodic solutions for nonlinear evolution equations in Banach space, Proc. AMS. 109 (1990), 653-661.
• [22] Y. Yamada, On nonlinear evolution equations generated by the subdifferential, J. Fac. Sci. Univ. Tokyo 23 (1976), 491-515.
• [23] S. Yotsutani, Evolution equations associated with the subdifferentials, J. Math. Soc. Japan 31 (1978), 623-646.