scholarly journals Non-Existence Results for Stable Solutions to Weighted Elliptic Systems Including Advection Terms

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 252
Author(s):  
Suleman Alfalqi
Keyword(s):  
Elliptic Systems ◽  
Existence Results ◽  
Liouville Type ◽  
Non Linear ◽  
Liouville Type Theorems ◽  
Stable Solutions ◽  
Bootstrap Iteration ◽  
Comparison Property

In this paper, we study a non-linear weighted Grushin system including advection terms. We prove some Liouville-type theorems for stable solutions of the system, based on the comparison property and the bootstrap iteration. Our results generalise and improve upon some previous works.

Liouville-type theorems and existence results for stable solutions to weighted Lane–Emden equations

2019 ◽  
Vol 150 (3) ◽  
pp. 1567-1579
Author(s):  
Alberto Farina ◽  
Shoichi Hasegawa
Keyword(s):  
Euclidean Space ◽  
Existence Result ◽  
Large Family ◽  
Existence Results ◽  
Liouville Type ◽  
Liouville Type Theorems ◽  
Stable Solutions

AbstractWe devote this paper to proving non-existence and existence of stable solutions to weighted Lane-Emden equations on the Euclidean space ℝN, N ⩾ 2. We first prove some new Liouville-type theorems for stable solutions which recover and considerably improve upon the known results. In particular, our approach applies to various weighted equations, which naturally appear in many applications, but that are not covered by the existing literature. A typical example is provided by the well-know Matukuma's equation. We also prove an existence result for positive, bounded and stable solutions to a large family of weighted Lane–Emden equations, which indicates that our Liouville-type theorems are somehow sharp.

scholarly journals Liouville Type Theorems for Stable Solutions of Certain Elliptic Systems

2012 ◽  
Vol 12 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Mostafa Fazly
Keyword(s):  
Elliptic Systems ◽  
Bounded Domains ◽  
Liouville Type ◽  
Liouville Type Theorems ◽  
Stable Solutions

AbstractWe establish Liouville type theorems for elliptic systems with various classes of nonlinearities on ℝis necessarily constant, whenever the dimension N < 8 + 3α +We also consider the case of bounded domains Ω ⊂ ℝ

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.

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