Multiple positive solutions to a three point third order boundary value problem
John R. Graef - Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, United States (email) Abstract: 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.
Keywords: Boundary value problems, existence of positive solutions, nonexistence
of positive solutions, nonlinear equations, three point problems, third order equations.
Received: September 2004; Revised: February 2005; Published: September 2005. |