Positive Solutions for Third Order Boundary Value Problems with p-Laplacian

Abstract.

We consider the following boundary value problem with nonhomogeneous three-point boundary condition

$$ \begin{array}{l} \left( {\phi _p ( {u^\prime } )} \right)^{\prime\prime} + a( t )f( u ) = 0, \quad t \in ( {0,1} ), \\ u( 0 ) = \xi u( \eta ) + \lambda , \quad u^\prime ( 0 ) = u^\prime( 1 ) = 0 \\ \end{array}$$

. We derive several existence, nonexistence, and multiplicity results for positive solutions in terms of different values of the parameter λ. The uniqueness of positive solutions and the dependence of positive solutions on the parameter λ are also studied.