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...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
Texas State University
2008-03-01
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Series: | Electronic Journal of Differential Equations |
Subjects: | |
Online Access: | http://ejde.math.txstate.edu/Volumes/2008/45/abstr.html |
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. |
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ISSN: | 1072-6691 |