Behaviour near zero and near infinity of solutions to elliptic equalities and inequalities

Abstract

Here we consider elliptic equations and inequalities involving quasilinear operators in divergence form and nonlinear lower order terms: $$-mathop{m div}left(mathcal{A}(x,u,abla u)ight) geq |x|^sigma u^Qquad(Q>0,sigma in mathbb{R}), $$ in dimension $Ngeq 3$. We study the asymptotic behaviour of the solutions and give {it a priori} estimate and non-existence results.

Keywords

• A priori estimates
• non-existence results
• degenerate quasilinear inequalities.