Existence of Positive Solution to Second-Order Three-Point BVPs on Time Scales. (28th September 2009)

• Record Type: Journal Article
• Authors: Sun, Jian-Ping
• Other Names: Perera Kanishka Academic Editor.
• Is Part Of: Boundary value problems. Volume 2009(2009)
• Publication Date: 2009-09-28
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2009/685040
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : We are concerned with the following nonlinear second-order three-point boundary value problem on time scales− x Δ Δ ( t ) = f ( t, x ( t ) ), t ∈ [ a, b ] 𝕋, x ( a ) = 0, x ( σ 2 ( b ) ) = δ x ( η ), wherea, b ∈ 𝕋 witha < b, η ∈ ( a, b ) 𝕋 and0 < δ < ( σ 2 ( b ) − a ) / ( η − a ) . A new representation of Green's function for the corresponding linear boundary value problem is obtained and some existence criteria of at least one positive solution for the above nonlinear boundary value problem are established by using the iterative method.