Uniqueness of Positive Solutions for a Class of Fourth-Order Boundary Value Problems. (29th May 2011)

• Record Type: Journal Article
• Authors: Caballero, J.; Harjani, J.; Sadarangani, K.
• Other Names: Rogovchenko Yuri V. Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2011(2011)
• Publication Date: 2011-05-29
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2011/543035
• Languages: English
• ISSNs: 1085-3375

Abstract

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.