## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Existence of periodic solutions for a nonautonomous differential equation

#### Abstract

We consider the nonautonomous differential equation of second order $x''+ a(t)x-b(t) x^l+c(t)x^{2k+1}=0$, where $a(t),b(t),c(t)$ are $T$-periodic functions and $2\leq l < 2k+1$. This is a generalization of a biomathematical model of an aneurysm in the circle of Willis. We prove the existence of a $T$-periodic solution for this equation, using a saddle-point theorem.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 2 (2012), 305-310.

Dates
First available in Project Euclid: 24 May 2012

https://projecteuclid.org/euclid.bbms/1337864274

Digital Object Identifier
doi:10.36045/bbms/1337864274

Mathematical Reviews number (MathSciNet)
MR2977233

Zentralblatt MATH identifier
1242.34070

#### Citation

Albuquerque de Araujo, Anderson Luis; Martins, Ricardo Miranda. Existence of periodic solutions for a nonautonomous differential equation. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 2, 305--310. doi:10.36045/bbms/1337864274. https://projecteuclid.org/euclid.bbms/1337864274