Green's Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument. (6th August 2014)

• Record Type: Journal Article
• Authors: Zhang, Xuemei; Feng, Meiqiang
• Other Names: Baleanu Dumitru Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-08-06
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/393187
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : This paper investigates the expression and properties of Green's function for a second-order singular boundary value problem with integral boundary conditions and delayed argument- x ′ ′ t - a t x ′ t + b t x t = ω t f t, x α t, t ∈ 0, 1 ; x ′ 0 = 0, x 1 - ∫ 0 1 h t x t d t = 0, wherea ∈ 0, 1, 0, + ∞, b ∈ C 0, 1, 0, + ∞ and, ω may be singular att = 0 or/and att = 1 . Furthermore, several new and more general results are obtained for the existence of positive solutions for the above problem by using Krasnosel'skii's fixed point theorem. We discuss our problems with a delayed argument, which may concern optimization issues of some technical problems. Moreover, the approach to express the integral equation of the above problem is different from earlier approaches. Our results cover a second-order boundary value problem without deviating arguments and are compared with some recent results.