The higher order quasilinear elliptic equation subject to Dirichlet boundary conditions may have unique and regular positive solution. If the domain is a ball, we obtain a priori estimate to the radial solutions via blowup. Extensions to systems and general domains are also presented. The basic ingredients are the maximum principle, Moser iterative scheme, an eigenvalue problem, a priori estimates by rescalings, sub/supersolutions, and Krasnosel′skiĭ fixed point theorem.
Marcelo Montenegro. "Positive solutions of higher order quasilinear elliptic equations." Abstr. Appl. Anal. 7 (8) 423 - 452, 12 September 2002. https://doi.org/10.1155/S1085337502204030