This paper studies the eigenvalue interval for the singular boundary value problem − u ′′ = g ( t , u ) + λ h ( 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.