## Bulletin of the Belgian Mathematical Society - Simon Stevin

- Bull. Belg. Math. Soc. Simon Stevin
- Volume 15, Number 2 (2008), 277-285.

### Multiple periodic solutions of some Liénard equations with p-Laplacian

#### Abstract

The existence, non-existence and multiplicity of solutions to periodic boundary value problems of Liénard type \begin{eqnarray*} (|u'|^{p-2}u')'+ f(u)u'+ g(u) = e(t) + s,\quad u(0)-u(T)=0=u'(0)-u'(T), \end{eqnarray*} is discussed, where $p>1,$ $f$ is arbitrary and $g$ is assumed to be bounded, positive and $g(\pm\infty)=0.$ The function $e$ is continuous on $[0,T]$ with mean value $0$ and $s$ is a parameter.

#### Article information

**Source**

Bull. Belg. Math. Soc. Simon Stevin, Volume 15, Number 2 (2008), 277-285.

**Dates**

First available in Project Euclid: 8 May 2008

**Permanent link to this document**

https://projecteuclid.org/euclid.bbms/1210254825

**Digital Object Identifier**

doi:10.36045/bbms/1210254825

**Mathematical Reviews number (MathSciNet)**

MR2424113

**Zentralblatt MATH identifier**

1160.34036

**Subjects**

Primary: 34B15: Nonlinear boundary value problems 34B16: Singular nonlinear boundary value problems 34C25: Periodic solutions

**Keywords**

p-Laplacian Liénard equations periodic solutions Leray-Schauder degree

#### Citation

Bereanu, Cristian. Multiple periodic solutions of some Liénard equations with p-Laplacian. Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 2, 277--285. doi:10.36045/bbms/1210254825. https://projecteuclid.org/euclid.bbms/1210254825