Asymptotic conditions for periodic solutions of ordinary differential equations

Ward, James R.

doi:10.1090/S0002-9939-1981-0597653-2

Asymptotic conditions for periodic solutions of ordinary differential equations
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by James R. Ward

Proc. Amer. Math. Soc. 81 (1981), 415-420

DOI: https://doi.org/10.1090/S0002-9939-1981-0597653-2

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Abstract:

We obtain sufficient conditions for the existence of periodic solutions to differential equations of the form \[ {x^{(m)}} + {a_{m - 1}}{x^{(m - 1)}} + \cdots + {a_1}x’ + g(t,x) = f(t)\quad (m \geqslant 1).\] 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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