Electron. J. Diff. Equ., Vol. 2010(2010), No. 177, pp. 1-8.

Lienard type p-Laplacian neutral Rayleigh equation with a deviating argument

Aomar Anane, Omar Chakrone, Loubna Moutaouekkil

Abstract:
Based on Manasevich-Mawhin continuation theorem, we prove the existence of periodic solutions for Lienard type $p$-Laplacian neutral Rayleigh equations with a deviating argument,
$$ (\phi_p(x(t)-c x(t-\sigma))')'+f(x(t))x'(t)+ g(t,x(t-\tau(t)))=e(t). $$
An example is provided to illustrate our results.

Submitted September 15, 2010. Published December 22, 2010.
Math Subject Classifications: 34C25, 34B15
Key Words: Periodic solution; neutral Rayleigh equation; Lienard equation; Deviating argument; p-Laplacian; Manasevich-Mawhin continuation.

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Aomar Anane
Université Mohamed I, Faculté des Sciences
Département de Mathématiques et Informatique
Oujda, Maroc
email: anane@sciences.univ-oujda.ac.ma
Omar Chakrone
Université Mohamed I, Faculté des Sciences
Département de Mathématiques et Informatique
Oujda, Maroc
email: chakrone@yahoo.fr
Loubna Moutaouekkil
Université Mohamed I, Faculté des Sciences
Département de Mathématiques et Informatique
Oujda, Maroc
email: loubna_anits@yahoo.fr

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