Periodic solutions of small period of systems of th order differential equations

Author:
Klaus Schmitt

Journal:
Proc. Amer. Math. Soc. **36** (1972), 459-463

MSC:
Primary 34C25

MathSciNet review:
0310351

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Abstract: This paper consists of a study of the existence of periodic solutions of systems of *n*th order ordinary differential equations using tools from degree theory.

**[1]**J. W. Bebernes and K. Schmitt,*Periodic boundary value problems for systems of second order differential equations*, J. Differential Equations**13**(1973), 32–47. MR**0340700****[2]**Erhard Heinz,*An elementary analytic theory of the degree of mapping in 𝑛-dimensional space*, J. Math. Mech.**8**(1959), 231–247. MR**0102580****[3]**M. A. Krasnosel′skiĭ,*The operator of translation along the trajectories of differential equations*, Translations of Mathematical Monographs, Vol. 19. Translated from the Russian by Scripta Technica, American Mathematical Society, Providence, R.I., 1968. MR**0223640****[4]**Klaus Schmitt,*Periodic solutions of nonlinear second order differential equations*, Math. Z.**98**(1967), 200–207. MR**0213653****[5]**Klaus Schmitt,*A note on periodic solutions of second order ordinary differential equations*, SIAM J. Appl. Math.**21**(1971), 491–494. MR**0304781****[6]**J. T. Schwartz,*Nonlinear functional analysis*, Gordon and Breach Science Publishers, New York-London-Paris, 1969. Notes by H. Fattorini, R. Nirenberg and H. Porta, with an additional chapter by Hermann Karcher; Notes on Mathematics and its Applications. MR**0433481****[7]**George Seifert,*A note on periodic solutions of second order differential equations without damping*, Proc. Amer. Math. Soc.**10**(1959), 396–398; errata, 1000. MR**0107057**, 10.1090/S0002-9939-1959-0107057-2

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DOI:
https://doi.org/10.1090/S0002-9939-1972-0310351-X

Keywords:
Periodic solutions,
degree theory

Article copyright:
© Copyright 1972
American Mathematical Society