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The existence of periodic solutions for systems of ordinary differential equations

Published online by Cambridge University Press:  22 January 2016

Yong-Hoon Lee
Yong-Hoon Lee*
Affiliation:
Department of Mathematics, Pusan National University, Pusan 609-735, Korea, [email protected]
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Abstract.

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We prove a multiplicity result of 2π-periodic solutions for certain weakly coupled system of ordinary differential equations with real parameters. The proofs are based on differential inequalities and coincidence degree.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 151 , September 1998 , pp. 145 - 160
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

References

[1] Ambrosetti, A. and Prodi, G., On the inversion of some differentiable mappings with singularities between Banach spaces, Ann. Mat. pura Appl., 4 (93) (1972), 231–247.Google Scholar
[2] Chiappinelli, R., Mawhin, J. and Nugari, R., Generalized Ambrosetti-Prodi conditions for nonlinear two-point boundary value problems, J. Diff. Equations, 69 (3) (1988), 422–434.Google Scholar
[3] Ding, S. H. and Mawhin, J., A multiplicity result for periodic solutions of higher order ordinary differential equations, Differential and Integral Equations, 1 (1) (1988), 31–39.Google Scholar
[4] Fabry, C., Mawhin, J. and Nkashama, M. N., A multiplicity result for periodic solutions of forced nonlinear second order ordinary differential equations, Bull. London Math. Soc, 18 (1986), 173–180.Google Scholar
[5] Hu, S. and Lakshmikantham, V., Periodic boundary value problems for second order impulsive differential systems, Nonlinear Analysis, T.M.A., 13 (1989), 75–85.Google Scholar
[6] Lee, Y.H., An Ambrosetti-Prodi type result for second order weakly coupled systems, Nonlinear Analysis T.M.A., 18 (8) (1992), 793–799.Google Scholar
[7] Mawhin, J., First order ordinary differential equations with several periodic solutions, J. Appl. Math. Physics, 38 (1987), 257–265.Google Scholar
[8] Mawhin, J., Topological degree methods in nonlinear boundary value problems, 40, CBMS Conference in Math, A.M.S. Providence R.I., 1979.Google Scholar
[9] Nkashama, M. N., A generalized upper and lower solution method and multiplicity results for nonlinear first order ordinary differential equations, J. Math. Anal. Appl., 140 (1989), 381–395.Google Scholar
[10] Ramos, M. and Sanchez, L., Multiple periodic solutions for some nonlinear ordinary differential equations of higher order, Differential and Integral Equations, 1 (2) (1989), 81–90.Google Scholar