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.