Existence results for singular nonlinear BVPs in the critical regime

We study the existence of solutions for a class of boundary value problems on the half line, associated to a third order ordinary differential equation governed by the Φ-Laplacian operator. The equation contains a Carathéodory function satisfying a weak growth condition of Winter-Nagumo type which is assumed to be continuous and it may vanish in a subset of zero Lebesgue measure, so that the problem can be singular. The approach we follow is based on fixed point techniques combined with the upper and lower solutions method.