Liouville results for stable solutions of weighted elliptic equations involving the Grushin operator

Mtaouaa, Wafa

doi:10.1007/s11587-024-00887-0

Ricerche mat

2024

DOI: 10.1007/s11587-024-00887-0

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Liouville results for stable solutions of weighted elliptic equations involving the Grushin operator

Wafa Mtaouaa

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2024

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Stable Solutions of a Class of Degenerate Elliptic Equations

Lang,

Liu

2024

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This paper deals with the second-order semi-linear degenerate elliptic equation yuyy+buy+Δxu+|u|α−1u=0,(x,y)∈Rn×(0,∞), where n≥1,α>1. We establish a Liouville theorem of stable solution of the degenerate equation mentioned above by using the energy method. The classification results for stable solutions belonging to C2 can be thought of as an analogue of the recent results of Farina for the Lane–Emden equation.

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Stable Solutions of a Class of Degenerate Elliptic Equations

Lang,

Liu

2024

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Liouville results for stable solutions of weighted elliptic equations involving the Grushin operator

Cited by 1 publication

References 24 publications

Stable Solutions of a Class of Degenerate Elliptic Equations

Stable Solutions of a Class of Degenerate Elliptic Equations

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