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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Periodic solutions of linear second order differential equations with deviating argument


Author: Klaus Schmitt
Journal: Proc. Amer. Math. Soc. 26 (1970), 282-285
MSC: Primary 34.75
MathSciNet review: 0265722
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0265722-5
Keywords: Periodic solutions, deviating argument, Eilenberg, Montgomery fixed point theorem
Article copyright: © Copyright 1970 American Mathematical Society