A priori estimates and reduction principles for quasilinear elliptic problems and applications

A priori estimate of of solutions of quasilinear elliptic equations are a subject of vital interest in recent years. Most of the results are dealing with nonnegative solutions and nonlinearities with denite sign. Recently, Serrin [25] considered Liouville theorems for quasilinear equations with source term changing sign. These results are consequence of appropriate a priori estimates on the possible solutions.