Exponentially harmonic maps, Morse index and Liouville type theorems

2019 ◽  
Vol 6 (4) ◽  
pp. 1388-1402
Author(s):  
Yuan-Jen Chiang
Keyword(s):  
Morse Index ◽  
Harmonic Maps ◽  
Liouville Type ◽  
Liouville Type Theorems

scholarly journals Liouville type theorems for p-harmonic maps

2008 ◽  
Vol 342 (1) ◽  
pp. 354-360 ◽  
Author(s):  
Dong Joo Moon ◽  
Huili Liu ◽  
Seoung Dal Jung
Keyword(s):  
Harmonic Maps ◽  
Liouville Type ◽  
Liouville Type Theorems

scholarly journals Finite Morse index solutions of the Hénon Lane–Emden equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Abdellaziz Harrabi ◽  
Cherif Zaidi
Keyword(s):  
Morse Index ◽  
Monotonicity Formula ◽  
Liouville Type ◽  
Emden Equation ◽  
Type Identity ◽  
Liouville Type Theorems ◽  
Whole Space ◽  
Stable Solutions ◽  
Pohozaev Type Identity

Abstract In this paper, we are concerned with Liouville-type theorems of the Hénon Lane–Emden triharmonic equations in whole space. We prove Liouville-type theorems for solutions belonging to one of the following classes: stable solutions and finite Morse index solutions (whether positive or sign-changing). Our proof is based on a combination of the Pohozaev-type identity, monotonicity formula of solutions and a blowing down sequence.

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