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Existence and Uniqueness of Positive Solution for a Singular Nonlinear Second-Order https://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq1_HTML.gif -Point Boundary Value Problem

Boundary Value Problems20102010:254928

DOI: 10.1155/2010/254928

Received: 25 November 2009

Accepted: 10 March 2010

Published: 31 March 2010

Abstract

The existence and uniqueness of positive solution is obtained for the singular second-order https://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq2_HTML.gif -point boundary value problem https://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq3_HTML.gif for https://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq4_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq5_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq6_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq7_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq8_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq9_HTML.gif are constants, and https://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq10_HTML.gif can have singularities for https://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq11_HTML.gif and/or https://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq12_HTML.gif and for https://static-content.springer.com/image/art%3A10.1155%2F2010%2F254928/MediaObjects/13661_2009_Article_908_IEq13_HTML.gif . The main tool is the perturbation technique and Schauder fixed point theorem.

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Authors’ Affiliations

(1)
Department of Mathematics, Beihua University

Copyright

© X. Lv and M. Pei. 2010

This article is published under license to BioMed Central Ltd. 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.