A priori estimates for nonlinear differential inequalities and applications

The aim of the paper is to derive a priori estimates and obtain the Harnack-type inequalities of positive weak solutions for the nonlinear differential inequalities in an exterior domain or interior domain. By using the test function method developed by Mitidieri and Pohozaev, we extend and improve some known results proved by Serrin and Zou, Bidaut-Véron and Pohozaev.