Classification of solutions to $-\Delta u=e^{-2u}$ in the half-space

Wei Dai; Zhao Liu; Berardino Sciunzi

doi:10.4171/rmi/1611

JournalsrmiVol. 42, No. 3pp. 1039–1058

Classification of solutions to $- Δ u = e^{- 2 u}$ in the half-space

Wei Dai
Beihang University (BUAA), Beijing, P. R. China; Ministry of Education, Beijing, P. R. China
Zhao Liu
Jiangxi Science and Technology Normal University, Nanchang, P. R. China
- zbMATH
- MR
Berardino Sciunzi
Università della Calabria (UNICAL), Arcavacata di Rende, Cosenza, Italy

$Classification of solutions to $-\Delta u=e^{-2u}$ in the half-space cover$

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Abstract

We classify all positive solutions to $- Δ u = e^{- 2 u}$ in the half space $R_{+}^{N}$ , under Dirichlet boundary condition.

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Wei Dai, Zhao Liu, Berardino Sciunzi, Classification of solutions to $- Δ u = e^{- 2 u}$ in the half-space. Rev. Mat. Iberoam. 42 (2026), no. 3, pp. 1039–1058

DOI 10.4171/RMI/1611