Potential systems with singular ϕ-Laplacian

In this paper, we are concerned with solvability of the boundary value problem [Formula: see text] where [Formula: see text] is a homeomorphism from [Formula: see text] — the open ball of radius [Formula: see text] centered at [Formula: see text] onto [Formula: see text], satisfying [Formula: see text], [Formula: see text], with [Formula: see text] of class [Formula: see text] on [Formula: see text], continuous and strictly convex on [Formula: see text] The potential [Formula: see text] is of class [Formula: see text] with respect to the second variable and [Formula: see text] is proper, convex and lower semicontinuous. We first provide a variational formulation in the frame of critical point theory for convex, lower semicontinuous perturbations of [Formula: see text]-functionals. Then, taking the advantage of this key step, we obtain existence of minimum energy as well as saddle-point solutions of the problem. Some concrete illustrative examples of applications are provided.