Twin solutions of even order boundary value problems for ordinary differential equations and finite difference equations.

摘要

The Avery-Henderson fixed-point theorem is first applied to obtain the existence of at least two positive solutions for the boundary value problem -1ny 2n=fy ,n=1,2,3&cdots;and t∈0,1 , with boundary conditions y2k 0=0y 2k+11 =0fork=0,1,2&cdots;, n-1. This theorem is subsequently used to obtain the existence of at least two positive solutions for the dynamic boundary value problem -1nD 2nuk guk ,n=1,2,3&cdots; andk∈ 0,&cdots;N, with boundary conditions D2k u0=0 D2k+1u N+1=0for k=0,1,2&cdots;,n-1.