TAILIEUCHUNG - Báo cáo hóa học: " PERIODIC SOLUTIONS OF SECOND-ORDER LIÉNARD EQUATIONS WITH p-LAPLACIAN-LIKE OPERATORS"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: PERIODIC SOLUTIONS OF SECOND-ORDER LIÉNARD EQUATIONS WITH p-LAPLACIAN-LIKE OPERATORS | PERIODIC SOLUTIONS OF SECOND-ORDER LIÉNARD EQUATIONS WITH p-LAPLACIAN-LIKE OPERATORS YOUYU WANG AND WEIGAO GE Received 12 April 2005 Accepted 10 August 2005 The existence of periodic solutions for second-order Lienard equations with p-Laplacian-like operator is studied by applying new generalization of polar coordinates. Copyright 2006 Y. Wang and W. Ge. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction In recent years the existence of periodic solutions for second-order Lienard equations u f u u u g u e t u u and its special case have been studied by many researchers we refer the readers to 1 3 4 6 7 9-12 and the references therein. Let us consider the so-called one-dimensional p-Laplacian operator ộp u where p 1 and ộp R R is given by ộp s IsIp--2s for s 0 and ộp 0 0. Periodic boundary conditions containing this operator have been considered in 2 5 . In 8 Manasevich and Mawhin investigated the existence of periodic solutions to some system cases involving the fairly general vector-valued operator ộ. They considerd the boundary value problem ộ u f t u u u 0 u T u 0 u T where the function ộ RN RN satisfies some monotonicity conditions which ensure that ộ is a homeomorphism onto RN. Recently in 16 we studied the existence of periodic solutions for the nonlinear differential equation with a p-Laplacian-like operator ộ u z f t u u 0. Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2006 Article ID 98685 Pages 1-17 DOI JIA 2006 98685 2 Periodic solutions for Lienard equations Motivated by the work of 13 in this paper we use new polar coordinates 13 to investigate the existence of periodic solutions for the second-order generalized Lienard equations with p-Laplacian-like operator ộ u f u ú u g u e t u u t G 0 T . Throughout this paper we always

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