## Differential and Integral Equations

### Periodic solutions and asymptotic behavior in Liénard systems with p-Laplacian operators

#### Abstract

We first prove the existence of periodic solutions to systems of the form $(\phi_{p}(u^{\prime}))^{\prime}+\frac{d}{dt}(\nabla F(u))+\nabla G(u)=e(t).$ We then study the asymptotic behavior of all solutions to such systems, and give sufficient conditions for uniform ultimate boundedness of solutions.

#### Article information

Source
Differential Integral Equations, Volume 22, Number 9/10 (2009), 979-998.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019518

Mathematical Reviews number (MathSciNet)
MR2553066

Zentralblatt MATH identifier
1240.34210

#### Citation

García-Huidobro, M.; Manásevich, R.; Ward, J.R. Periodic solutions and asymptotic behavior in Liénard systems with p-Laplacian operators. Differential Integral Equations 22 (2009), no. 9/10, 979--998. https://projecteuclid.org/euclid.die/1356019518