Existence Results for Higher-Order Boundary Value Problems on Time Scales. (29th July 2009)

• Record Type: Journal Article
• Authors: Liu, Jian; Sang, Yanbin
• Other Names: Otero-Espinar Victoria Academic Editor.
• Is Part Of: Advances in difference equations. Volume 2009(2009)
• Publication Date: 2009-07-29
• Subjects: Difference equations -- Periodicals; 515.625
• DOI: 10.1155/2009/209707
• Languages: English
• ISSNs: 1687-1847

Abstract

Abstract : By using the fixed-point index theorem, we consider the existence of positive solutions for the following nonlinear higher-order four-point singular boundary value problem on time scalesu Δ n ( t ) + g ( t ) f ( u ( t ), u Δ ( t ), …, u Δ n − 2 ( t ) ) = 0, 0 < t < T ;u Δ i ( 0 ) = 0, 0 ≤ i ≤ n − 3 ;α u Δ n − 2 ( 0 ) − β u Δ n − 1 ( ξ ) = 0, n ≥ 3 ;γ u Δ n − 2 ( T ) + δ u Δ n − 1 ( η ) = 0, n ≥ 3, whereα > 0, β ≥ 0, γ > 0, δ ≥ 0, ξ, η ∈ ( 0, T ), ξ < η, andg : ( 0, T ) → [ 0, + ∞ ) is rd-continuous.