Electron. J. Diff. Equ., Vol. 2013 (2013), No. 205, pp. 1-9.

Periodic solutions for fourth-order p-Laplacian functional differential equations with sign-variable coefficient

Jiaying Liu, Wenbin Liu, Bingzhuo Liu

Abstract:
Using the theory of coincidence degree, we show the existence of periodic solutions to the fourth-order p-Laplacian differential equations of Lienard-type
$$ \phi_p(x''))''+f(x(t))x'(t)+\alpha(t)g_1(x(t-\tau_1(t,x(t)))) +\beta(t)g_2(x(t-\tau_1(t,x(t))))=p(t). $$
The rate of growth of $g_1(u)$ with respect to the variable u is allowed to be greater than p-1, and the coefficient $\beta (t)$ is allowed to change sign.

Submitted October 7, 2012. Published September 18, 2013.
Math Subject Classifications: 34A12, 34C25.
Key Words: p-Laplacian equation; periodic solution; multiple deviating argument; Mawhin continuation theorem.

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Jiaying Liu
Department of Mathematics
China University of Mining and Technology
Xuzhou, Jiangsu 221116, China
email: relinaliu@163.com
Wenbin Liu
Department of Mathematics
China University of Mining and Technology
Xuzhou, Jiangsu 221116, China
email: wblium@163.com
Bingzhuo Liu
Department of Mathematics
China University of Mining and Technology
Xuzhou, Jiangsu 221116, China
email: tuteng3839@163.com

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