ON THE SOLVABILITY OF A NONSELFADJOINT QUASILINEAR ELLIPTIC BOUNDARY VALUE PROBLEM

Abstract

A solvability theorem is obtained for a quasilinear elliptic boundary value problem. The linear part of the problem is an elliptic operator of order 2m which has a nontrivial kernel not necessarily symmetric. The nonlinear part may grow sublinearly and contain derivatives of order up to 2m. The proof is based on Borsuk’s Theorem and the Nussbaum–Sodovskii degree.