Topological Degree Methods for Partial Differential Operators in Generalized Sobolev Spaces

The main aim of this paper is to prove, by using the topological degree methods, the existence of solutions for nonlinear elliptic equation Au = f where Au = Sigma(vertical bar alpha vertical bar<m) (-1)(vertical bar alpha vertical bar)D(alpha)A(alpha)(x, u, del u, ..., del(m)u) is partial differential operators of general divergence form and f is an element of W--m,W-p'(.) (Omega) with p(x) is an element of (1, infinity).