Liouville comparison principles for solutions of semilinear elliptic second-order partial differential inequalities

Abstract

The purpose of this work is to obtain new Liouville comparison principles for entire weak solutions of semilinear elliptic second-order partial differential inequalities of the forms and on ℝ n , where n ≥ 2, q > 0 and ℒ is a linear (possibly non-uniformly) elliptic partial differential operator of second order in divergence form, in terms of the behaviour of the coefficients of the operator ℒ at infinity in a function space directly associated with ℒ.