Existence and Multiple Solutions for Nonlinear Second-Order Discrete Problems with Minimum and Maximum. (29th July 2008)

• Record Type: Journal Article
• Authors: Ma, Ruyun; Gao, Chenghua
• Other Names: Staněk Svatoslav Academic Editor.
• Is Part Of: Advances in difference equations. Volume 2008(2008)
• Publication Date: 2008-07-29
• Subjects: Difference equations -- Periodicals; 515.625
• DOI: 10.1155/2008/586020
• Languages: English
• ISSNs: 1687-1847

Abstract

Abstract : Consider the multiplicity of solutions to the nonlinear second-order discrete problems with minimum and maximum:Δ 2 u ( k − 1 ) = f ( k, u ( k ), Δ u ( k ) ), k ∈ T, min { u ( k ) : k ∈ T ^ } = A, max ⁡ { u ( k ) : k ∈ T ^ } = B, wheref : T × ℝ 2 → ℝ, a, b ∈ ℕ are fixed numbers satisfyingb ≥ a + 2, and A, B ∈ ℝ are satisfyingB > A, T = { a + 1, …, b − 1 }, T ^ = { a, a + 1, …, b − 1, b } .