On the Dirichlet problem for weakly non-linear elliptic partial differential equations
Edward Norman Dancer · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1977
Synopsis We study the existence of solutions of the Dirichlet problem for weakly nonlinear elliptic partial differential equations. We only consider cases where the nonlinearities do not depend on any partial derivatives. For these cases, we prove the existence of solutions for a wide variety of nonlinearities.