A priori estimate for lower solutions of a class quasilinear elliptic equations

1999 ◽  
Vol 20 (2) ◽  
pp. 231-232
Author(s):  
Wang Xiangdong ◽  
Han Puxian ◽  
Liang Xiting
Keyword(s):  
Elliptic Equations ◽  
A Priori ◽  
A Priori Estimate ◽  
Quasilinear Elliptic Equations ◽  
Priori Estimate ◽  
Quasilinear Elliptic

scholarly journals Positive solutions of higher order quasilinear elliptic equations

2002 ◽  
Vol 7 (8) ◽  
pp. 423-452
Author(s):  
Marcelo Montenegro
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
A Priori Estimate ◽  
Higher Order ◽  
Dirichlet Boundary Conditions ◽  
Quasilinear Elliptic Equations ◽  
Radial Solutions ◽  
The Maximum Principle ◽  
Priori Estimates ◽  
Quasilinear Elliptic

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.

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