The existence of at least three positive solutions for differential equation ( ϕ p ( u ′ ( t ) ) ) ′ + g ( t ) f ( t , u ( t ) , u ′ ( t ) ) = 0 , under one of the following boundary conditions: u ( 0 ) = ∑ i = 1 m − 2 a i u ( ξ i ) , φ p ( u ′ ( 1 ) ) = ∑ i = 1 m − 2 b i φ p ( u ′ ( ξ i ) ) or φ p ( u ′ ( 0 ) ) = ∑ i = 1 m − 2 a i φ p ( u ′ ( ξ i ) ) , u ( 1 ) = ∑ i = 1 m − 2 b i u ( ξ i ) is obtained by using the H. Amann fixed point theorem, where φ p ( s ) = | s | p − 2 s , p > 1 , 0 < ξ 1 < ξ 2 < ⋯ < ξ m − 2 < 1 , a i > 0 , b i > 0 , 0 < ∑ i = 1 m − 2 a i < 1 , 0 < ∑ i = 1 m − 2 b i < 1 . The interesting thing is that g ( t ) may be singular at any point of [0,1] and f may be noncontinuous.