A singular boundary value problem for a degenerate elliptic PDE

We consider a singular boundary value problem associated with the ∞∞-Laplacian and having nonseparable inhomogeneous term. We establish the existence of ground state solutions to such a problem in bounded domains as well as in the whole Euclidean space. The investigation is based on subsolution and supersolution methods and existence of principal eigenfunctions to the eigenvalue problem of Dirichlet type corresponding to the ∞∞-Laplacian.