Existence of Periodic Solution for p-Laplacian Neutral Rayleigh Equation with Sign-variable Coefficient of Non Linear Term

As p-Laplacian equations have been widely applied in field of the fluid mechanics and nonlinear elastic mechanics, it is necessary to investigate the periodic solutions of functional differential equations involving the scalar p-Laplacian. By using Mawhin’s continuation theorem, we study the existence of periodic solutions for p-Laplacian neutral Rayleigh equation (ϕp(x(t)−c(t)x(t − r))) + f(x(t)) + g1(x(t − τ1(t, |x|∞))) + β(t)g2(x(t − τ2(t, |x|∞))) = e(t), It is meaningful that the functions c(t) and β(t) are allowed to change
signs in this paper, which are different from the corresponding ones of known literature.

• Aomar Anane
• Omar Chakrone
• Loubna Moutaouekkil

• periodic solution
• neutral Rayleigh equation
• variable sign
• Deviating argument
• p-Laplacian
• Mawhin’s continuation.

<p>[1] W. Cheug, J.L. Ren, Periodic solutions for p-Laplacian type Rayleigh
equations, Nonlinear Anal.65(2006)2003-2012.
[2] Changxiu Song, Xuejun Gao , Periodic solutions for p-Laplacian functional
differential equations with two deviating arguments, Electron. J.
Diff. Equ., Vol. 2011 (2011), No. 140, pp. 1-8.
[3] Liang Feng, Guo Lixiang, Lu Shiping, Existence of periodic solutions
for a p-Laplacian neutral functional differential equation, Nonlinear
Analysis 71(2009)427-436.
[4] R.E. Gaines, J.L. Mawhin , Coincidence Degree and Nonlinear Differential
Equations (M), Springer Verlag, Berlin, 1977.
[5] C. Zhong, X. Fan, W. Chen, Introduction to Nonlinear Functional
Analysis (M), Lanzhou University Press, Lan Zhou, 2004 (in Chinese).</p>