Application of Topological Methods to Quasilinear Parabolic Boundary-Value Problems

We apply a topological approach to the investigation of quasilinear parabolic boundary-value problems. The class of problems under investigation is reduced to an operator equation with an operator satisfying condition (S)₊. We establish theorems on solvability and give an example of the application of the approach indicated to the case of second-order parabolic equations.