Periodic solutions for dissipative-repulsive systems

Tohoku Mathematical Journal

Volumn 52, Issue 3, 2000, Pages 321-329

  Küpper, Tassilo ^a   Li, Yong ^b   Zhang, Bo ^c  

^a UNIVERSITY OF COLOGNE   (Germany)

^b JILIN UNIVERSITY   (China)

^c FAYETTEVILLE STATE UNIVERSITY   (United States)

Author keywords

Brouwer degree; Dissipative repulsive system; Periodic solution

Indexed keywords

EID: 0034259098     PISSN: 00408735     EISSN: None     Source Type: Journal    
DOI: 10.2748/tmj/1178207816     Document Type: Article

References (16)

1. O. A. Arino, T. A. Burton and J. R. Haddock, Periodic solutions to functional differential equations, Proc. Roy. Soc. Edingburgh Sect. A 101 (1985), 253-271.
2. T. A. Burton and S. N. Zhang, Unified boundedness, periodicity and stability in ordinary and functional differential equations, Ann. Mat. Pura Appl. (4) 145 (1986), 129-158.
3. A. Capieto, J. Mawhin and F. Zanolin, Continuation theorem for periodic perturbations of autonomous systems, Trans. Amer. Math. Soc. 329 (1992), 41-72.
4. L. H. Erbe, W. Krawcewicz and J. H. Wu, Leray-Schauder degree for semilinear Fredholm maps and periodic boundary value problems of neutral equations, Nonlinear Anal. 15 (1990), 747-764.
5. L. H. Erbe, W. Krawcewicz and J. H. Wu, A composite coincidence degree with applications to boundary value problems of neutral equations, Trans. Amer. Math. Soc. 335 (1993), 459-478.
6. J. K. Hale and O. Lopes, Fixed point theorems and dissipative processes, J. Differential Equations 13 (1973), 391-402.
7. J. Hofbauer and K. Sigmund, Dynamical Systems and the Theory of Evolution, Cambridge Univ. Press, Cambridge-New York, 1988.
8. V. Hutson, The existence of an equilibrium for permanent systems, Rocky Mountain J. Math. 20 (1990), 1033-1040.
9. A. M. Krasnosel’skii, M. A. Krasnosel’skii, J. Mawhin and A. Pokrovskii, Generalized guiding functions in a problem on high frequency forced oscillations, Nonlinear Anal. 22 (1994), 1357-1371.
10. Y. Li and Z. H. Lin, Periodic solutions of differential inclusions, Nonlinear Anal. 24 (1995), 631-741.
11. Y. Li and X. R. Lu, Continuation theorems to boundary value problems, J. Math. Anal. Appl. 190 (1995), 32-49.
12. Y. Li, Q. D. Zhou and X. R. Lu, Periodic solutions and equilibrium states for functional differential inclusions with nonconvex right hand side, Quart. Appl. Math. 55 (1997), 57-68.
13. G. Makay, Periodic solutions of dissipative functional differential equations, Tohoku Math. J. 46 (1994), 417-426.
14. J. Mawhin, Existence of periodic solutions for higher order differential systems that are not of class D, J. Differential Equations 8 (1970), 523-530.
15. T. Yoshizawa, Stability Theory by Liapunov’s Second Method, The Mathematical Society of Japan, Tokyo, 1966.
16. P. Zabreiko and M. Krasnosel’skii, Iteration of operators and fixed points, Dokl. Akad. Nauk SSSR 196(1971), 1006-1009.