Positive solutions to a fourth order three point boundary value problem
John R. Graef - Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States (email)
Abstract: We consider a three-point boundary value problem for the beam equation. Some a priori estimates to the positive solutions for the boundary value problem are obtained. Sufficient conditions for the existence and nonexistence of positive solutions for the boundary value problem are established. The results are illustrated with an example.
Keywords: Fixed point theorem, cone, nonlinear boundary-value problem, positive solution
Received: September 2008; Revised: February 2009; Published: September 2009.