Journal of Applied Mathematics 
Volume 2005 (2005), Issue 1, Pages 1-21
doi:10.1155/JAM.2005.1

Periodic boundary value problems for nth-order ordinary differential equations with p-laplacian

Yuji Liu1,2 and Weigao Ge3

 1Department of Mathematics, Hunan Institute of Science and Technology, Yueyang, Hunan 414000, China
2Department of Applied Mathematics, Beijing Institute of Technology, Beijing 1000811, China
3Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, China
Received 26 April 2004; Revised 5 September 2004

Abstract

We prove existence results for solutions of periodic boundary value problems concerning the nth-order differential equation with p-Laplacian [φ(x(n−1)(t))]'=f(t,x(t),x'(t),...,x(n−1)(t)) and the boundary value conditions x(i)(0)=x(i)(T), i=0,...,n−1. Our method is based upon the coincidence degree theory of Mawhin. It is interesting that f may be a polynomial and the degree of some variables among x0,x1,...,xn−1 in the function f(t,x0,x1,...,xn−1) is allowed to be greater than 1.