# American Institute of Mathematical Sciences

2005, 2005(Special): 337-344. doi: 10.3934/proc.2005.2005.337

## Multiple positive solutions to a three point third order boundary value problem

 1 Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States 2 Department of Mathematics and Statistics, Kennesaw State University, Kennesaw, GA 30144, United States

Received  September 2004 Revised  February 2005 Published  September 2005

The authors consider the boundary value problem $$\begin{cases} u'''(t) = q(t)f(u), \quad 0 < t < 1, \\ u(0) = u'(p) = u''(1) = 0, \end{cases}$$ where $p \in(\frac{1}{2},1)$ is a constant. They give sufficient conditions for the existence of multiple positive solutions to this problem. In so doing, they are able to improve some recent results on this problem. Examples are included to illustrate the results.
Citation: John R. Graef, Bo Yang. Multiple positive solutions to a three point third order boundary value problem. Conference Publications, 2005, 2005 (Special) : 337-344. doi: 10.3934/proc.2005.2005.337
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