Approximation of a quasilinear elliptic equation with nonlinear boundary condition
Timothy R. Cranny · Bulletin of the Australian Mathematical Society · 1994
We consider a quasilinear elliptic partial differential equation with nonlinear boundary condition under assumptions which do not allow the application of standard degree theory results or techniques such as the method of continuity. An approximation using mollifiers is introduced, allowing the application of Leray-Schauder degree theory, and homotopy arguments are then used to prove the existence of solutions to the approximating problems. A subsequent paper will discuss the question of the convergence of these approximate solutions to a classical solution of the original problem.