Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
844595 | Nonlinear Analysis: Theory, Methods & Applications | 2007 | 14 Pages |
Abstract
In this paper, we study m-point boundary value problems for higher order ordinary differential equation {y(2n)(t)=f(t,y(t),yâ³(t),â¦,y(2(nâ1))(t)),0â¤tâ¤1,y(2i)(0)=0,y(2i)(1)=âj=1mâ2kijy(2i)(ξj),0â¤iâ¤nâ1, where f is allowed to change sign, and 0=ξ0<ξ1<ξ2<â¯<ξmâ2<ξmâ1=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.
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Authors
Yanping Guo, Jiwei Tian,