Abstract
Vazquez in 1984 established a strong maximum principle for the classical m-Laplace differential inequality Δ mu−f(u)≤0, where Δ m u=div(| Du| m−2 Du) and f( u) is a non-decreasing continuous function with f(0)=0. We extend this principle to a wide class of singular inequalities involving quasilinear divergence structure elliptic operators, and also consider the converse problem of compact support solutions in exterior domains.
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