Existence of a weak solutions to a class of nonlinear parabolic problems via topological degree method

Abstract

In this paper, we study the existence of "weak solutions" for a class of nonlinear parabolic problems of the type ∂ u⁄∂ t - div Α (x, t, ∇ u) = Φ (x, t) + div B(x, t, u, ∇ u). Using Berkovits and Mustonen's topological degree theory, we demonstrate the existence of a weak solutions to the problems under consideration in the space Lp(0, T, W01, p(Ω)), where Ω is a bounded domain in RN, N ≥ 2 and p ≥ 2.