Entire solutions of the inequality div\((A| Du|)Du\geqq f(u)\)
This paper is concerned with quasilinear elliptic inequalities of the form \[ \text{div}(A(|Du|)Du)\geq f(u),\quad x\in\mathbb{R}^N, \] where \(f\not\equiv 0\) is a nonnegative continuous function on \([0,\infty)\) vanishing only at zero. Typical functions \(A\) we are interested in, are \[ A(p)= p^{m-2},\quad m>1,\quad A(p)= (1+p^2)^{-\alpha},\quad \alpha\leq 1/2, \] and so on. We obtain existence and nonexistence criteria of nonnegative nontrivial entire solutions of the inequality.
scientific article; zbMATH DE number 1028183