Fractional elliptic systems with critical nonlinearities

Nonlinearity ◽  
2021 ◽  
Vol 34 (11) ◽  
pp. 7540-7573
Author(s):  
Mousomi Bhakta ◽  
Souptik Chakraborty ◽  
Olimpio H Miyagaki ◽  
Patrizia Pucci
Keyword(s):  
Elliptic Systems ◽  
Critical Nonlinearities

scholarly journals Critical elliptic systems involving multiple strongly–coupled Hardy–type terms

2019 ◽  
Vol 9 (1) ◽  
pp. 866-881
Author(s):  
Dongsheng Kang ◽  
Mengru Liu ◽  
Liangshun Xu
Keyword(s):  
Explicit Form ◽  
Elliptic Equations ◽  
Elliptic Systems ◽  
Asymptotic Behaviors ◽  
Strongly Coupled ◽  
Critical Nonlinearities ◽  
Hardy Type ◽  
Analysis Methods ◽  
Least Energy Solutions ◽  
Least Energy

Abstract In this paper, we study the radially–symmetric and strictly–decreasing solutions to a system of critical elliptic equations in RN, which involves multiple critical nonlinearities and strongly–coupled Hardy– type terms. By the ODEs analysis methods, the asymptotic behaviors at the origin and infinity of solutions are proved. It is found that the singularities of u and v in the solution (u, v) are at the same level. Finally, an explicit form of least energy solutions is found under certain assumptions, which has all of the mentioned properties for the radial decreasing solutions.

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