Solutions of nonlinear elliptic equations in unbounded Lipschitz domains
Pablo Amster, María-Cristina Mariani, Osvaldo Méndez · Forum Mathematicum · 2007
This work is devoted to the study of the elliptic equation Δ u = f ( x, u ) in an exterior non-smooth domain. Applying the method of upper and lower solutions and a diagonal argument, we prove the existence of solutions under various boundary conditions.