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Publicly Available Published by De Gruyter March 10, 2016

Periodic Solutions of Singular Nonlinear Perturbations of the Ordinary p-Laplacian

  • P. Jebelean and J. Mawhin

Abstract

Using some recent extensions of upper and lower solutions techniques and continuation theorems to the periodic solutions of quasilinear equations of p-Laplacian type, we prove the existence of positive periodic solutions of equations of the form

(|xʹ|p-2xʹ)ʹ + f(x)xʹ + g(x) = h(t)

with p > 1, f arbitrary and g singular at 0. This extends results of Lazer and Solimini for the undamped ordinary differential case.

Published Online: 2016-03-10
Published in Print: 2002-08-01

© 2016 by Advanced Nonlinear Studies, Inc.

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