The paper discusses the existence of positive solutions, dead core solutions, and pseudo dead core solutions of the singular problem ( φ ( u ′ ) ) ′ + f ( t , u ′ ) = λ g ( t , u , u ′ ) , u ′ ( 0 ) = 0 , β u ′ ( T ) + α u ( T ) = A . Here λ is a positive parameter, β ≥ 0 , α , A > 0 , f may be singular at t = 0 and g is singular at u = 0 .