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Proceedings of the American Mathematical Society

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

 

 

Asymptotic conditions for periodic solutions of ordinary differential equations


Author: James R. Ward
Journal: Proc. Amer. Math. Soc. 81 (1981), 415-420
MSC: Primary 34C25
DOI: https://doi.org/10.1090/S0002-9939-1981-0597653-2
MathSciNet review: 597653
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Abstract: We obtain sufficient conditions for the existence of periodic solutions to differential equations of the form

$\displaystyle {x^{(m)}} + {a_{m - 1}}{x^{(m - 1)}} + \cdots + {a_1}x' + g(t,x) = f(t)\quad (m \geqslant 1).$

The conditions are necessary for some classes of functions, and require no growth condition on $ g(t,x)$ for $ x \geqslant 0(x \leqslant 0)$.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0597653-2
Keywords: Periodic solutions, nonlinear equations, coincidence degree
Article copyright: © Copyright 1981 American Mathematical Society