## Abstract and Applied Analysis

### Periodic Solutions of Second-Order Differential Inclusions Systems with $p(t)$-Laplacian

#### Abstract

The existence of periodic solutions for nonautonomous second-order differential inclusion systems with $p(t)$-Laplacian is considered. We get some existence results of periodic solutions for system, $(d/dt)({|\stackrel{˙}{u}(t)|}^{p(t)-2}\stackrel{˙}{u}(t))\in \partial F(t,u(t))$ a.e. $t\in [0,T]$, $u(0)-u(T)=\stackrel{˙}{u}(0)-\stackrel{˙}{u}(T)=0$, by using nonsmooth critical point theory. Our results generalize and improve some theorems in the literature.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 475956, 24 pages.

Dates
First available in Project Euclid: 28 March 2013

https://projecteuclid.org/euclid.aaa/1364475910

Digital Object Identifier
doi:10.1155/2012/475956

Mathematical Reviews number (MathSciNet)
MR2994932

Zentralblatt MATH identifier
1261.34021

#### Citation

Zhang, Liang; Zhang, Peng. Periodic Solutions of Second-Order Differential Inclusions Systems with $p(t)$ -Laplacian. Abstr. Appl. Anal. 2012 (2012), Article ID 475956, 24 pages. doi:10.1155/2012/475956. https://projecteuclid.org/euclid.aaa/1364475910

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