Existence of Triple Positive Solutions for Second-Order Discrete Boundary Value Problems. (4th January 2007)

• Record Type: Journal Article
• Authors: Guo, Yanping; Zhang, Jiehua; Ji, Yude
• Is Part Of: Discrete dynamics in nature and society. Volume 2007(2007)
• Publication Date: 2007-01-04
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2007/60534
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : By using a new fixed-point theorem introduced by Avery and Peterson (2001), we obtain sufficient conditions for the existence of at least three positive solutions for the equationΔ 2 x ( k − 1 ) + q ( k ) f ( k, x ( k ), Δ x ( k ) ) = 0, fork ∈ { 1, 2, …, n − 1 }, subject to the following two boundary conditions:x ( 0 ) = x ( n ) = 0 orx ( 0 ) = Δ x ( n − 1 ) = 0, wheren ≥ 3 .