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Bull. Korean Math. Soc. 2012; 49(3): 455-463

Printed May 1, 2012

https://doi.org/10.4134/BKMS.2012.49.3.455

Copyright © The Korean Mathematical Society.

Anti-periodic solutions for higher-order Li\'{e}nard type differential equation with $p$-Laplacian operator

Taiyong Chen and Wenbin Liu

China University of Mining and Technology, China University of Mining and Technology

Abstract

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In this paper, by using degree theory, we consider a kind of higher-order Li\'{e}nard type $p$-Laplacian differential equation as follows \begin{eqnarray*} (\phi_p(x^{(m)}))^{(m)}+f(x)x'+g(t,x)=e(t). \end{eqnarray*} 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

MSC numbers: 34B15, 34C25

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