scholarly journals Liouville Type Theorems, Monotonicity Results and a Priori Bounds for Positive Solutions of Elliptic Systems

2005 ◽  
pp. 599-628 ◽  
Author(s):  
Djairo G. de Figueiredo ◽  
Boyan Sirakov
Keyword(s):  
Positive Solutions ◽  
A Priori ◽  
Elliptic Systems ◽  
A Priori Bounds ◽  
Liouville Type ◽  
Liouville Type Theorems ◽  
Monotonicity Results

scholarly journals Monotonicity and rigidity of solutions to some elliptic systems with uniform limits

2019 ◽  
Vol 22 (05) ◽  
pp. 1950044 ◽  
Author(s):  
Alberto Farina ◽  
Berardino Sciunzi ◽  
Nicola Soave
Keyword(s):  
A Priori ◽  
Elliptic Systems ◽  
A Priori Bounds ◽  
Liouville Type ◽  
Liouville Type Theorems ◽  
Regularity Results

In this paper, we prove the validity of Gibbons’ conjecture for a coupled competing Gross–Pitaevskii system. We also provide sharp a priori bounds, regularity results and additional Liouville-type theorems.

scholarly journals Semilinear Elliptic Systems With Exponential Nonlinearities in Two Dimensions

2006 ◽  
Vol 6 (2) ◽  
Author(s):  
Djairo G. de Figueiredo ◽  
João Marcos do Ó ◽  
Bernhard Ruf
Keyword(s):  
Positive Solutions ◽  
A Priori ◽  
Elliptic Systems ◽  
Two Dimensions ◽  
Smooth Domain ◽  
A Priori Bounds ◽  
Semilinear Elliptic Systems ◽  
Semilinear Elliptic

AbstractWe establish a priori bounds for positive solutions of semilinear elliptic systems of the formwhere Ω is a bounded and smooth domain in ℝ

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.

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