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October 2020 Existence of entire radial large solutions for a class of Monge–Ampère type equations and systems
Zhijun Zhang, Hanxue Liu
Rocky Mountain J. Math. 50(5): 1893-1899 (October 2020). DOI: 10.1216/rmj.2020.50.1893

Abstract

This paper is mainly concerned with existence of entire positive radial large solutions for a class of Monge–Ampère type equations:

det D 2 u ( x ) α Δ u = a ( | x | ) f ( u ) , x N ,

and systems:

det D 2 u ( x ) α Δ u = a ( | x | ) f ( v ) , x N , det D 2 v ( x ) β Δ v = b ( | x | ) g ( u ) , x N ,

where detD2u is the so-called Monge–Ampère operator, Δ is the classical Laplace operator, N2, α,β are positive constants, f,g:[0,)[0,) are continuous and nondecreasing, and a,b:N[0,) are continuous.

Citation

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Zhijun Zhang. Hanxue Liu. "Existence of entire radial large solutions for a class of Monge–Ampère type equations and systems." Rocky Mountain J. Math. 50 (5) 1893 - 1899, October 2020. https://doi.org/10.1216/rmj.2020.50.1893

Information

Received: 29 April 2019; Accepted: 2 April 2020; Published: October 2020
First available in Project Euclid: 5 November 2020

zbMATH: 07274845
MathSciNet: MR4170697
Digital Object Identifier: 10.1216/rmj.2020.50.1893

Subjects:
Primary: 35J55, 35J60
Secondary: 35J65, 35J96

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 5 • October 2020
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