On periodic solutions of nonlinear differential equations with singularities

Abstract:

Necessary and sufficient conditions for existence of periodic solutions of differential equations containing singularities are given. Our theorems apply to $u'' + 1/{u^\alpha } = h\left ( t \right ) \equiv h\left ( {t + T} \right )$ for all $\alpha > 0$ and to $u'' - 1/{u^\alpha } = h\left ( t \right )$ if $\alpha \geq 1$, and for this case $\alpha \geq 1$ is an essential condition.