A priori estimates, existence and Liouville theorems for semilinear elliptic systems with power nonlinearities

2014 ◽  
Vol 102 ◽  
pp. 144-158 ◽  
Author(s):  
Pavol Quittner
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Systems ◽  
Liouville Theorems ◽  
Semilinear Elliptic Systems ◽  
Semilinear Elliptic ◽  
Priori Estimates

Liouville theorems for elliptic inequalities and applications

1998 ◽  
Vol 128 (6) ◽  
pp. 1217-1247 ◽  
Author(s):  
Isabeau Birindelli ◽  
Enzo Mitidieri
Keyword(s):  
Blow Up ◽  
A Priori ◽  
Elliptic Systems ◽  
Bounded Domains ◽  
Systems Of Equations ◽  
Liouville Theorems ◽  
Semilinear Elliptic Systems ◽  
Semilinear Equations ◽  
Semilinear Elliptic ◽  
Elliptic Inequalities

In this paper we prove nonexistence of positive C2 solutions for systems of semilinear elliptic inequalities, for polyharmonic semilinear inequalities in cones and, under better conditions on the nonlinearity, for bounded positive solutions of elliptic semilinear equations in half spaces. Using a blow-up argument, these results allow us to prove a-priori bounds for a class of semilinear elliptic systems of equations in bounded domains.

Positive Solutions for Elliptic Equations With Supercritical Nonlinearity

2009 ◽  
Vol 9 (3) ◽  
Author(s):  
Paulo Rabelo
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Auxiliary Problem ◽  
Semilinear Elliptic Equation ◽  
Minimax Methods ◽  
Semilinear Elliptic ◽  
Priori Estimates ◽  
Supercritical Nonlinearity

AbstractIn this paper minimax methods are employed to establish the existence of a bounded positive solution for semilinear elliptic equation of the form−∆u + V (x)u = P(x)|u|where the nonlinearity has supercritical growth and the potential can change sign. The solutions of the problem above are obtained by proving a priori estimates for solutions of a suitable auxiliary problem.

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.

Sign in / Sign up

Export Citation Format

Share Document