On Nonexistence of Nonnegative Solutions for Some Quasilinear Elliptic Inequalities in a Bounded Domain

Abstract

Using the test function method, we study sufficient conditions of nonexistence of nonnegative solutions for a quasilinear elliptic inequality of the form \( -\text{div}(u^r|D u|^{p-2} D u) \geq a(x)u^q|D u|^s \) in a bounded domain and its generalizations.