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

An approximation approach to eigenvalue intervals for singular boundary value problems with sign changing and superlinear nonlinearities

Haishen Lü1 , Ravi P. Agarwal2 and Donal O'Regan3

1Department of Applied Mathematics, Hohai University, Nanjing 210098, China
 2Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901-6975, USA
 3Department of Mathematics, National University of Ireland, Galway, Ireland

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.