Periodic boundary value problems fornth-order ordinary differential equations withp-laplacian

[摘要] We prove existence results for solutions of periodic boundary value problems concerning thenth-order differential equationwithp-Laplacian[φ(x(n−1)(t))]'=f(t,x(t),x'(t),...,x(n−1)(t))and the boundary value conditionsx(i)(0)=x(i)(T),i=0,...,n−1. Our method is based upon the coincidence degree theory of Mawhin. It is interesting thatfmay be a polynomial and the degree of some variables amongx0,x1,...,xn−1in the functionf(t,x0,x1,...,xn−1)is allowed to be greater than1.

[学科分类] 应用数学