Open Access

An Approximation Approach to Eigenvalue Intervals for Singular Boundary Value Problems with Sign Changing and Superlinear Nonlinearities

Boundary Value Problems20092009:103867

DOI: 10.1155/2009/103867

Received: 25 June 2009

Accepted: 5 October 2009

Published: 26 October 2009

Abstract

This paper studies the eigenvalue interval for the singular boundary value problem https://static-content.springer.com/image/art%3A10.1155%2F2009%2F103867/MediaObjects/13661_2009_Article_825_IEq1_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2F2009%2F103867/MediaObjects/13661_2009_Article_825_IEq2_HTML.gif may be singular at https://static-content.springer.com/image/art%3A10.1155%2F2009%2F103867/MediaObjects/13661_2009_Article_825_IEq3_HTML.gif ,   https://static-content.springer.com/image/art%3A10.1155%2F2009%2F103867/MediaObjects/13661_2009_Article_825_IEq4_HTML.gif , and may change sign and be superlinear at https://static-content.springer.com/image/art%3A10.1155%2F2009%2F103867/MediaObjects/13661_2009_Article_825_IEq5_HTML.gif . The approach is based on an approximation method together with the theory of upper and lower solutions.

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Authors’ Affiliations

(1)
Department of Applied Mathematics, Hohai University
(2)
Department of Mathematical Sciences, Florida Institute of Technology
(3)
KFUPM Chair Professor, Mathematics and Statistics Department, King Fahd University of Petroleum and Minerals
(4)
Department of Mathematics, National University of Ireland

Copyright

© Haishen Lü et al. 2009

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.