Existence and Uniqueness of Solutions for Higher-Order Three-Point Boundary Value Problems. (19th August 2009)

• Record Type: Journal Article
• Authors: Pei, Minghe; Chang, Sung Kag
• Other Names: Perera Kanishka Academic Editor.
• Is Part Of: Boundary value problems. Volume 2009(2009)
• Publication Date: 2009-08-19
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2009/362983
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : We are concerned with the higher-order nonlinear three-point boundary value problems:x ( n ) = f ( t, x, x ′, …, x ( n − 1 ) ), n ≥ 3, with the three point boundary conditionsg ( x ( a ), x ′ ( a ), …, x ( n − 1 ) ( a ) ) = 0 ;x ( i ) ( b ) = μ i, i = 0, 1, …, n − 3 ; h ( x ( c ), x ′ ( c ), …, x ( n − 1 ) ( c ) ) = 0, wherea < b < c, f : [ a, c ] × ℝ n → ℝ = ( − ∞, + ∞ ) is continuous, g, h : ℝ n → ℝ are continuous, andμ i ∈ ℝ, i = 0, 1, …, n − 3 are arbitrary given constants. The existence and uniqueness results are obtained by using the method of upper and lower solutions together with Leray-Schauder degree theory. We give two examples to demonstrate our result.