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Abstrakty
The paper presents a geometric method of finding periodic solutions of retarded functional differential equations (REDE) x'(t) = f(t,x1), where f is T-periodic in t. We construct a pair of subsets of R x R^n called a T-periodic block and compute its Lefschetz number. If it is nonzero, then there exists a T-periodic solution.
Wydawca
Rocznik
Tom
Strony
353--363
Opis fizyczny
Bibliogr. 10 poz.
Twórcy
autor
- Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland, pawlowsk@im.uj.edu.pl
Bibliografia
- [1] K. Borsuk, Theory of Retracts, Monogr. Mat. 44, PWN, Warszawa, 1967.
- [2] C. Bowszyc, Fixed point theorems for the pairs of spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. 16 (1968), 845-850.
- [3] C. Conley, Isolated Invariant Sets and the Morse Index, CBMS Reg. Conf. Ser. Math. 38, Amer. Math. Soc., Providence, RI, 1978.
- [4] A. Dold, Lectures on Algebraic Topology, Springer, Berlin, 1980.
- [5] A. Granas, The Leray-Schauder index and the fixed point theory for arbitrary ANRs, Bull. Soc. Math. France 100 (1972), 209-228.
- [6] J. Hale, Theory of Functional Differential Equations, Appl. Math. Sci. 3, Springer, New York, 1977.
- [7] K. P. Rybakowski, Ważewski's principle for retarded functional differential equations, J. Differential Equations 36 (1980), 117-138.
- [8] R. Srzednicki, A geometric method for the periodic problem in ordinary differentia equations, Sém. Anal. Moderne, Univ. de Sherbrooke, 1992.
- [9] -, Periodic and bounded solutions in blocks for time-periodic nonautonomous ordinary differential equations, Nonlinear Anal. 22 (1994), 707-737.
- [10] T. Ważewski, Sur un principe topologique de l'examen de l'allure asymptotique des intégrales des équations différentielles ordinaires, Ann. Soc. Polon. Math. 20 (1947), 279-313.
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Bibliografia
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bwmeta1.element.baztech-article-BAT5-0005-0002