A PRIORI ESTIMATES AND EXISTENCE FOR QUASILINEAR ELLIPTIC EQUATIONS WITH NONLINEAR NEUMANN BOUNDARY CONDITIONS
Hu, Z, Li Wang, Peihao Zhao, Hu, Z (reprint author), Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China. · Lanzhou University Institutional Repository · 2016
This article concerns the existence of positive solutions for a nonlinear Neumann problem involving the m-Laplacian. The equation does not have a variational structure. We use a blow-up argument and a Liouville-type theorem to obtain a priori estimates and obtain the existence of positive solutions by the Krasnoselskii fixed point theorem.