Positive solutions for the $Phi$-Laplacian when $Phi$ is a sup - multiplicative - like function

We provide sufficient conditions for the existence of positive solutions of a boundary-value problem for a one dimensional $Phi$-Laplacian ordinary differential equation with deviating arguments, where $Phi$ is a sup-multiplicative-like function (in a sense introduced here) and the boundary conditions include nonlinear expressions at the end points. For this end, we use the Krasnoselskii fixed point theorem in a cone. The results obtained improve and generalize known results in [17] and elsewhere.