Local solvability of fully nonlinear parabolic problems of higher order

Abstract

The paper is devoted to reduction of fully nonlinear parabolic problems of high order to operator equations involving operator satisfying (S₊) condition. The topological methods could be used to investigate solvability of such operator equations. The theorems of uniqueness and local existence for solution of boundary value problem, proved by topological approach are formulated in the paper. The results formulated are generalizations of analogous facts proved in [1].