Multiple positive solutions for nonlinear second-order m-point boundary-value problems with sign changing nonlinearities

In this paper, we study the nonlinear second-order m-point boundary value problem $$displaylines{ u''(t)+f(t,u)=0,quad 0leq t leq 1, cr eta u(0)-gamma u'(0)=0,quad u(1)=sum _{i=1}^{m-2}alpha_{i} u(xi_{i}), }$$ where the nonlinear term $f$ is allowed to change sign. We impose...

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Bibliographic Details
Main Authors: Fuyi xu, Zhenbo Chen, Feng Xu
Format: Article
Language:English
Published: Texas State University 2008-03-01
Series:Electronic Journal of Differential Equations
Subjects:
Online Access:http://ejde.math.txstate.edu/Volumes/2008/45/abstr.html
Description
Summary:In this paper, we study the nonlinear second-order m-point boundary value problem $$displaylines{ u''(t)+f(t,u)=0,quad 0leq t leq 1, cr eta u(0)-gamma u'(0)=0,quad u(1)=sum _{i=1}^{m-2}alpha_{i} u(xi_{i}), }$$ where the nonlinear term $f$ is allowed to change sign. We impose growth conditions on $f$ which yield the existence of at least two positive solutions by using a fixed-point theorem in double cones. Moreover, the associated Green's function for the above problem is given.
ISSN:1072-6691