scholarly journals Uniform a priori estimates for positive solutions of higher order Lane-Emden equations in $\mathbb{R}^n$

2021 ◽  
Vol 65 ◽  
pp. 319-333
Author(s):  
Wei Dai ◽  
Thomas Duyckaerts
Keyword(s):  
Positive Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Higher Order ◽  
Priori Estimates

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.

scholarly journals Quasilinear elliptic systems in divergence form associated to general nonlinearities

2018 ◽  
Vol 7 (4) ◽  
pp. 425-447 ◽  
Author(s):  
Lorenzo D’Ambrosio ◽  
Enzo Mitidieri
Keyword(s):  
Positive Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Systems ◽  
Divergence Form ◽  
Systems Of Equations ◽  
Quasilinear Elliptic Systems ◽  
Open Set ◽  
Priori Estimates ◽  
Quasilinear Elliptic

AbstractThe paper is concerned with a priori estimates of positive solutions of quasilinear elliptic systems of equations or inequalities in an open set of {\Omega\subset\mathbb{R}^{N}} associated to general continuous nonlinearities satisfying a local assumption near zero. As a consequence, in the case {\Omega=\mathbb{R}^{N}}, we obtain nonexistence theorems of positive solutions. No hypotheses on the solutions at infinity are assumed.

scholarly journals A priori estimates for higher order multipliers on a circle

2002 ◽  
Vol 130 (10) ◽  
pp. 3043-3050 ◽  
Author(s):  
A. Alexandrou Himonas ◽  
Gerard Misiołek
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Higher Order ◽  
Priori Estimates

scholarly journals Existence and a Priori Estimates for Positive Solutions of p-Laplace Systems

2002 ◽  
Vol 184 (2) ◽  
pp. 422-442 ◽  
Author(s):  
Céline Azizieh ◽  
Philippe Clément ◽  
Enzo Mitidieri
Keyword(s):  
Positive Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Priori Estimates
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