# ANTI-PERIODIC SOLUTIONS FOR HIGHER-ORDER LIÉENARD TYPE DIFFERENTIAL EQUATION WITH p-LAPLACIAN OPERATOR

• Chen, Taiyong ;
• Liu, Wenbin
• Published : 2012.05.31
• 54 8

#### Abstract

In this paper, by using degree theory, we consider a kind of higher-order Li$\acute{e}$enard type $p$-Laplacian differential equation as follows $$({\phi}_p(x^{(m)}))^{(m)}+f(x)x^{\prime}+g(t,x)=e(t)$$. Some new results on the existence of anti-periodic solutions for above equation are obtained.

#### Keywords

anti-periodic solution;higher-order differential equation;p-Laplacian operator;Leray-Schauder principle

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