## Differential and Integral Equations

### Necessary and sufficient conditions for the existence of periodic solutions of second-order ordinary differential equations with singular nonlinearities

#### Abstract

We introduce necessary and sufficient conditions for the existence of periodic solutions of the equation $$u'' + f(u)u' + g(u) = h(t),$$ where $g$ has a singularity of repulsive type at the origin and $f$ is arbitrary.

#### Article information

Source
Differential Integral Equations, Volume 8, Number 7 (1995), 1843-1858.

Dates
First available in Project Euclid: 12 May 2013

https://projecteuclid.org/euclid.die/1368397762

Mathematical Reviews number (MathSciNet)
MR1347985

Zentralblatt MATH identifier
0831.34048

Subjects
Primary: 34C25: Periodic solutions
Secondary: 34B15: Nonlinear boundary value problems

#### Citation

Omari, Pierpaolo; Ye, Wei Yin. Necessary and sufficient conditions for the existence of periodic solutions of second-order ordinary differential equations with singular nonlinearities. Differential Integral Equations 8 (1995), no. 7, 1843--1858. https://projecteuclid.org/euclid.die/1368397762