Harnack inequality for nonlinear elliptic equations with strong absorption

We develop Harnack inequalities for two different types of equations. First we consider a fully nonlinear uniformly elliptic equation related to the Pucci’s maximal and the minimal operators. Next we consider a quasilinear equation related to the p-Laplacian. In both cases we consider lower order terms of Keller–Osserman type. Although the equations considered are quite different, we employ a unified method to approach both problems and the results we find are similar.