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

The aim of this paper is to study the oscillation of solutions of the nonlinear degenerate elliptic equation in the Heisenberg group H n . We first derive a critical inequality in H n . Based on it, we establish a Picone-type differential inequality and a Sturm-type comparison principle. Then we obt...

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Veröffentlicht in:	Boundary value problems 2021-04, Vol.2021 (1), p.1-9, Article 40
Hauptverfasser:	Wu, Duan, Niu, Pengcheng
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Approximations and Expansions Difference and Functional Equations Elliptic functions Heisenberg group Mathematics Mathematics and Statistics Nonlinear degenerate elliptic equation Ordinary Differential Equations Oscillation Partial Differential Equations Picone-type inequality Sturm-type comparison principle Theorems
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Beschreibung
Zusammenfassung:	The aim of this paper is to study the oscillation of solutions of the nonlinear degenerate elliptic equation in the Heisenberg group H n . We first derive a critical inequality in 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 .
ISSN:	1687-2770 1687-2762 1687-2770
DOI:	10.1186/s13661-021-01516-7