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Positive Solutions for Nonlinear https://static-content.springer.com/image/art%3A10.1155%2F2007%2F74517/MediaObjects/13661_2006_Article_661_IEq1_HTML.gif th-Order Singular Nonlocal Boundary Value Problems

Boundary Value Problems20072007:074517

DOI: 10.1155/2007/74517

Received: 23 June 2006

Accepted: 26 January 2007

Published: 5 April 2007

Abstract

We study the existence and multiplicity of positive solutions for a class of https://static-content.springer.com/image/art%3A10.1155%2F2007%2F74517/MediaObjects/13661_2006_Article_661_IEq2_HTML.gif th-order singular nonlocal boundary value problems https://static-content.springer.com/image/art%3A10.1155%2F2007%2F74517/MediaObjects/13661_2006_Article_661_IEq3_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2007%2F74517/MediaObjects/13661_2006_Article_661_IEq4_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2007%2F74517/MediaObjects/13661_2006_Article_661_IEq5_HTML.gif where https://static-content.springer.com/image/art%3A10.1155%2F2007%2F74517/MediaObjects/13661_2006_Article_661_IEq6_HTML.gif . The singularity may appear at https://static-content.springer.com/image/art%3A10.1155%2F2007%2F74517/MediaObjects/13661_2006_Article_661_IEq7_HTML.gif and/or https://static-content.springer.com/image/art%3A10.1155%2F2007%2F74517/MediaObjects/13661_2006_Article_661_IEq8_HTML.gif . The Krasnosel'skii-Guo theorem on cone expansion and compression is used in this study. The main results improve and generalize the existing results.

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Authors’ Affiliations

(1)
Department of Mathematics, Qufu Normal University
(2)
Department of Mathematics and Statistics, Curtin University of Technology

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Copyright

© Xin’an Hao et al. 2007

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.