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
DOI:
https://doi.org/10.1090/S0002-9939-1970-0265722-5
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.
- Samuel Eilenberg and Deane Montgomery, Fixed point theorems for multi-valued transformations, Amer. J. Math. 68 (1946), 214–222. MR 16676, DOI https://doi.org/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 https://doi.org/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
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Keywords:
Periodic solutions,
deviating argument,
Eilenberg,
Montgomery fixed point theorem
Article copyright:
© Copyright 1970
American Mathematical Society