Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument

Abstract and Applied Analysis, Aug 2014

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 , where and, may be singular at or/and at . 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.

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Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument

Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument Xuemei Zhang1 and Meiqiang Feng2 1Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China 2School of Applied Science, Beijing Information Science & Technology University, Beijing 100192, China Received 16 May 2014; Revised 15 July 2014; Accepted 16 July 2014; Published 6 August 2014 Academic Editor: Dumitru Baleanu Copyright © 2014 Xuemei Zhang and Meiqiang Feng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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Xuemei Zhang, Meiqiang Feng. Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument, Abstract and Applied Analysis, 2014, 2014, DOI: 10.1155/2014/393187