Twin positive solutions for higher order m-point boundary value problems with sign changing nonlinearities

摘要

A new fixed point theorem on double cones is applied to obtain the existence of at least two positive solutions for the 2nd order m-point boundary value problemy(2n)(t)=f(t,y(t),y′′(t),…,y(2(n−1))(t)),0⩽t⩽1,y(2i)(0)−βiy(2i+1)(0)=0,y(2i)(1)=∑j=1m−2kijy(2i)(ξj),0⩽i⩽n−1,where f is allowed to change sign, 0<ξ1<ξ2<⋯<ξm−2<1. The associated Green’s function for the above problem is also given.