Article ID Journal Published Year Pages File Type
844595 Nonlinear Analysis: Theory, Methods & Applications 2007 14 Pages PDF
Abstract
In this paper, we study m-point boundary value problems for higher order ordinary differential equation {y(2n)(t)=f(t,y(t),y″(t),…,y(2(n−1))(t)),0≤t≤1,y(2i)(0)=0,y(2i)(1)=∑j=1m−2kijy(2i)(ξj),0≤i≤n−1, where f is allowed to change sign, and 0=ξ0<ξ1<ξ2<⋯<ξm−2<ξm−1=1. We show sufficient conditions for the existence of at least two positive solutions by applying a new fixed point theorem in cones and the associated Green's function. In particular, the second positive solutions for the above problem is not concave.
Related Topics
Physical Sciences and Engineering Engineering Engineering (General)
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