Uniqueness of Positive Solutions for a Class of Fourth-Order Boundary Value Problems. (29th May 2011) - Caballero, J.; Harjani, J.; Sadarangani, K.
Abstract : The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fourth-order boundary value problem:y ( 4 ) ( t ) = f ( t, y ( t ) ), t ∈ [ 0, 1 ], y ( 0 ) = y ( 1 ) = y ′ ( 0 ) = y ′ ( 1 ) = 0 . Moreover, under certain assumptions, we will prove that the above boundary value problem has a unique symmetric positive solution. Finally, we present some examples and we compare our results with the ones obtained in recent papers. Our analysis relies on a fixed point theorem in partially ordered metric spaces.