Existence of positive solutions for singular fourth-order three-point boundary value problems

• Published in: Advances in difference equations Vol. 2013; no. 1; p. 51
• Main Authors: Sun, Yan, Zhu, Cun
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 08.03.2013; BioMed Central Ltd
• Subjects: Analysis; Difference and Functional Equations; Functional Analysis; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Partial Differential Equations; existence; positive solution; cone; boundary value problems

In this article, we consider the boundary value problem u ( 4 ) ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , subject to the boundary conditions u ( 0 ) = u ′ ( 0 ) = u ″ ( 0 ) = 0 and u ″ ( 1 ) − α u ″ ( η ) = λ . In this setting, 0 < η < 1 and α ∈ [ 0 , 1 η ) are constants and λ ∈ [ 0 ,...