We introduce a new method for proving the nonexistence of positive supersolutions of
elliptic inequalities in unbounded domains of ℝ n. The simplicity and robustness of our
maximum principle-based argument provides for its applicability to many elliptic inequalities
and systems, including quasilinear operators such as the p-Laplacian, and nondivergence
form fully nonlinear operators such as Bellman-Isaacs operators. Our method gives new and
optimal results in terms of the nonlinear functions appearing in the inequalities, and applies …

We introduce a new method for proving the nonexistence of positive supersolutions of
elliptic inequalities in the whole space Rn as well as exterior domains. The simplicity and
robustness of our maximum principlebased argument provides for its applicability to many
elliptic inequalities and systems, including quasilinear operators such as the p-Laplacian,
and nondivergence form fully nonlinear operators such as Bellman-Isaacs operators. Our
method gives new and optimal results in terms of the nonlinear functions appearing in the …