Nonlinear elliptic inequalities with gradient terms on the Heisenberg group

2015 ◽  
Vol 121 ◽  
pp. 262-279 ◽  
Author(s):  
Sara Bordoni ◽  
Roberta Filippucci ◽  
Patrizia Pucci
Keyword(s):  
Heisenberg Group ◽  
Nonlinear Elliptic ◽  
Elliptic Inequalities

scholarly journals An oscillation theorem for the nonlinear degenerate elliptic equation in the Heisenberg group

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Duan Wu ◽  
Pengcheng Niu
Keyword(s):  
Elliptic Equation ◽  
Heisenberg Group ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Degenerate Elliptic Equation ◽  
Oscillation Theorem ◽  
Nonlinear Elliptic ◽  
Degenerate Elliptic ◽  
Oscillation Of Solutions ◽  
Nonlinear Degenerate

AbstractThe aim of this paper is to study the oscillation of solutions of the nonlinear degenerate elliptic equation in the Heisenberg group $H^{n}$ H n . We first derive a critical inequality in $H^{n}$ H n . Based on it, we establish a Picone-type differential inequality and a Sturm-type comparison principle. Then we obtain an oscillation theorem. Our result generalizes the related conclusions for the nonlinear elliptic equations in $R^{n}$ R n .

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