Open Access
12 September 2002 Positive solutions of higher order quasilinear elliptic equations
Marcelo Montenegro
Abstr. Appl. Anal. 7(8): 423-452 (12 September 2002). DOI: 10.1155/S1085337502204030


The higher order quasilinear elliptic equation Δ(Δp(Δu))=f(x,u) 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.


Download Citation

Marcelo Montenegro. "Positive solutions of higher order quasilinear elliptic equations." Abstr. Appl. Anal. 7 (8) 423 - 452, 12 September 2002.


Published: 12 September 2002
First available in Project Euclid: 14 April 2003

zbMATH: 1044.35021
MathSciNet: MR1930826
Digital Object Identifier: 10.1155/S1085337502204030

Primary: 35A05 , 35J55
Secondary: 35J60

Rights: Copyright © 2002 Hindawi

Vol.7 • No. 8 • 12 September 2002
Back to Top