Divergent type quasilinear Dirichlet problem with singularities (Q852001)

The Dirichlet problem is considered for a quasilinear elliptic equation with singular data and singular coefficients. The authors use the Leray-Schauder fixed point theorem in the framework of nets of equations with a priori estimates controlled by the growth-order of constants in these estimates. They transfer and improve some results from the classical theory of quasi-linear elliptic problems given by \textit{D. Gilbarg} and \textit{N. S. Trudinger} in [Elliptic partial differential equations of second-order (Springer-Verlag, 1983; Zbl 0562.35001)] in the frame of a certain generalized function algebra.