Dear Colleagues,

We continue our Colloquium in the Math Department.

*************************

John R. Graef and Lingju Kong*

Department of Mathematics,
University of Tennessee at Chattanooga
Chattanooga, TN

Tuesday, February 14, EMCS 422, 3:00 pm.

A Necessary and Sufficient Condition for Existence of Positive Solutions
of Nonlinear Boundary Value Problems

Abstract. We study the nonlinear boundary value problem

$(\phi(u''))''=f(t,u,u',u''),\; \; t\in
(0,1),\;\;u^{(2i)}(0)=u^{(2i)}(1)=0,\;i=0,1,$

and obtain a necessary and sufficient condition for the existence of
symmetric positive solutions. We also discuss the application of our result
to the special case where $f$ is a power function of $u$ and its
derivatives. Our analysis mainly relies on the lower and upper solution
method.

* the speaker

The talk is accessible to students who have had an introduction to
differential equations.

*************************************

Boris P Belinskiy,

Colloquium Committee

Department of Mathematics, Dept. 6956

University of Tennessee at Chattanooga

Ph. (423) 425-4748

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