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

Abstract

Abstract The 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 $R^{n}$ .

Keywords

• Heisenberg group
• Nonlinear degenerate elliptic equation
• Picone-type inequality
• Sturm-type comparison principle
• Oscillation