This paper investigates the singular differential equation ( p ( t ) u ′ ) ′ = p ( t ) f ( u ) , having a singularity at t = 0 . The existence of a strictly increasing solution (a homoclinic solution) satisfying u ′ ( 0 ) = 0 , u ( ∞ ) = L > 0 is proved provided that f has two zeros and a linear behaviour near − ∞ .