Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 205, pp. 1-9.
Title: Periodic solutions for fourth-order $p$-Laplacian functional
differential equations with sign-variable coefficient}
Authors: Jiaying Liu (China Univ, of Mining and Tech., Xuzhou, Jiangsu, China)
Wenbin Liu (China Univ, of Mining and Tech., Xuzhou, Jiangsu, China)
Bingzhuo Liu (China Univ, of Mining and Tech., Xuzhou, Jiangsu, China)
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.