Spectral and stochastic properties of the $f$-Laplacian, solutions of   PDE's at infinity, and geometric applications
  The aim of this paper is to suggest a new viewpoint to study qualitative properties of solutions of semilinear elliptic PDE's defined outside a compact set. The relevant tools come from spectral theory and from a combination of stochastic properties of the relevant differential operators. Possible links between spectral and stochastic properties are analyzed in detail. 
G. Pacelli Bessa, Stefano Pigola and Alberto G. Setti
math.DG