Periodic solutions of linear second order differential equations with deviating argument
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- by Klaus Schmitt
- Proc. Amer. Math. Soc. 26 (1970), 282-285
- DOI: https://doi.org/10.1090/S0002-9939-1970-0265722-5
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Abstract:
This paper is concerned with the question of the existence of periodic solutions of periodic linear second order differential equations with deviating argument. Using a fixed point theorem for multivalued mappings and results concerning boundary value problems for such equations, we prove that the existence of periodic solutions of both types of differential inequalities implies the existence of periodic solutions. This result, in turn, is used to obtain the existence of periodic solutions of certain nonlinear differential equations with deviating argument.References
- Samuel Eilenberg and Deane Montgomery, Fixed point theorems for multi-valued transformations, Amer. J. Math. 68 (1946), 214–222. MR 16676, DOI 10.2307/2371832
- L. J. Grimm and Klaus Schmitt, Boundary value problems for delay-differential equations, Bull. Amer. Math. Soc. 74 (1968), 997–1000. MR 228785, DOI 10.1090/S0002-9904-1968-12114-7 —, Boundary value problems for differential equations with deviating arguments, Aequationes Math. 3 (1969), 24-38.
- Solomon Lefschetz, Topics in Topology, Annals of Mathematics Studies, No. 10, Princeton University Press, Princeton, N. J., 1942. MR 0007094
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 26 (1970), 282-285
- MSC: Primary 34.75
- DOI: https://doi.org/10.1090/S0002-9939-1970-0265722-5
- MathSciNet review: 0265722