Potential bounds in problems on quasilinear elliptic equations

We study quasilinear elliptic equations with strong nonlinear terms and sys tems of such equations. The methods developed by the authors in [1], [2] ar e used to prove the existence of solutions for boundary - value problems us ing some information on behavior of potential bounds for nonlinearities; th e L-characteristics of elliptic operators and their fractional powers play an important role. New conditions are suggested for the existence of classi cal solutions of quasilinear second order elliptic equations.