Singular problems on the half–line∗

The paper investigates singular nonlinear problems arising in hydro-dynamics. In particular, it deals with the problem on the half–line of the form (p(t)u′(t)) ′ = p(t)f(u(t)), u′(0) = 0, u(∞) = L. The existence of a strictly increasing solution (a homoclinic solution) of this problem is proved by the dynamical systems approach and the lower and upper functions method