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

The existence of triple positive solutions for a boundary-value problem governed by the $Phi$-Laplacian is investigated, when $Phi$ is a so-called sup-multiplicative-like function (in a sense introduced in [22]) and the boundary conditions include nonlinear expressions at the end points (as in [21, 28]). The Leggett-Williams fixed point theorem in a cone is used. The results improve and generalize known results given in [21].