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

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

MathSciNet review:
0310351

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Abstract | References | Similar Articles | Additional Information

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 (to appear). MR**0340700 (49:5451)****[2]**E. Heinz,*An elementary analytic theory of the degree of mapping in n-dimensional space*, J. Math. Mech.**8**(1959), 231-247. MR**21**#1370. MR**0102580 (21:1370)****[3]**M. A. Krasnosel'skii,*The operator of translation along trajectories of differential equations*, ``Nauka", Moscow, 1966; English transl., Transl. Math. Monographs, vol. 19, Amer. Math. Soc., Providence, R.I., 1968. MR**34**#3012; MR**36**#6688. MR**0223640 (36:6688)****[4]**K. Schmitt,*Periodic solutions of nonlinear second order differential equations*, Math. Z.**98**(1967), 200-207. MR**35**#4511. MR**0213653 (35:4511)****[5]**-,*A note on periodic solutions of second order ordinary differential equations*, SIAM J. Appl. Math.**21**(1971), 491-494. MR**0304781 (46:3913)****[6]**J. T. Schwartz,*Nonlinear functional analysis*, Gordon and Breach, New York, 1969. MR**0433481 (55:6457)****[7]**G. Seifert,*A note on periodic solutions of second order differential equations without damping*, Proc. Amer. Math. Soc.**10**(1959), 396-398; errata, 1000. MR**21**#5784. MR**0107057 (21:5784)**

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Additional Information

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

Keywords:
Periodic solutions,
degree theory

Article copyright:
© Copyright 1972
American Mathematical Society