The paper discusses the existence of positive solutions, dead-core solutions, and pseudo-dead-core solutions of the singular problem ( ϕ ( u ′ ) ) ′ = λ f ( t , u , u ′ ) , u ( 0 ) - α u ′ ( 0 ) = A , u ( T ) + β u ′ ( 0 ) + γ u ′ ( T ) = A . Here λ is a positive parameter, α > 0 , A > 0 , β ≥ 0 , γ ≥ 0 , f is singular at u = 0, and f may be singular at u ' = 0 .