Boundary Value Problems
Volume 2009 (2009), Article ID 103867, 34 pages
doi:10.1155/2009/103867
Research Article

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

Haishen Lü,1 Ravi P. Agarwal,2,3 and Donal O'Regan4

1Department of Applied Mathematics, Hohai University, Nanjing 210098, China
2Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901-6975, USA
3KFUPM Chair Professor, Mathematics and Statistics Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
4Department of Mathematics, National University of Ireland, Galway, Ireland

Received 25 June 2009; Accepted 5 October 2009

Academic Editor: Ivan T. Kiguradze

Copyright © 2009 Haishen Lü et al. 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.

Abstract

This paper studies the eigenvalue interval for the singular boundary value problem −u′′=g(t,u)+λh(t,u),   t∈(0,1),  u(0)=0=u(1), where g+h may be singular at u=0,  t=0,1, and may change sign and be superlinear at u=+∞. The approach is based on an approximation method together with the theory of upper and lower solutions.