ON THE SOLVABILITY OF SOME PARABOLIC EQUATIONS INVOLVING NONLINEAR BOUNDARY CONDITIONS WITH L¹ DATA.

We analyze the existence of solutions for a class of quasilinear parabolic equations with critical growth nonlinearities, nonlinear boundary conditions, and L¹ data. We formulate our problems in an abstract form, then using some techniques of functional analysis, such as Leray-Schauder's topological degree associated with the truncation method and very interesting compactness results, we establish the existence of weak solutions to the proposed models. [ABSTRACT FROM AUTHOR]