Nonexistence of positive supersolutions to a class of semilinear elliptic equations and systems in an exterior domain

Huyuan Chen; Rui Peng; Feng Zhou

doi:10.1007/s11425-018-9447-y

Nonexistence of positive supersolutions to a class of semilinear elliptic equations and systems in an exterior domain

Huyuan Chen, Rui Peng^*, Feng Zhou

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

In this paper, we consider the following semilinear elliptic equation: {−Δu=h(x,u)inΩ,u⩾0on∂Ω, where Ω is an exterior domain in ℝ^N with N ⩾ 3, h: Ω × ℝ⁺ → ℝ is a measurable function, and derive optimal nonexistence results of positive supersolutions. Our argument is based on a nonexistence result of positive supersolutions of a linear elliptic problem with Hardy potential. We also establish sharp nonexistence results of positive supersolutions to an elliptic system.

Original language	English
Pages (from-to)	1307-1322
Number of pages	16
Journal	Science China Mathematics
Volume	63
Issue number	7
DOIs	https://doi.org/10.1007/s11425-018-9447-y
State	Published - 1 Jul 2020

Keywords

35B53
35J60
nonexistence
semilinear elliptic problem
supersolution

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10.1007/s11425-018-9447-y

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title = "Nonexistence of positive supersolutions to a class of semilinear elliptic equations and systems in an exterior domain",

abstract = "In this paper, we consider the following semilinear elliptic equation: \{−Δu=h(x,u)inΩ,u⩾0on∂Ω, where Ω is an exterior domain in ℝN with N ⩾ 3, h: Ω × ℝ+ → ℝ is a measurable function, and derive optimal nonexistence results of positive supersolutions. Our argument is based on a nonexistence result of positive supersolutions of a linear elliptic problem with Hardy potential. We also establish sharp nonexistence results of positive supersolutions to an elliptic system.",

keywords = "35B53, 35J60, nonexistence, semilinear elliptic problem, supersolution",

author = "Huyuan Chen and Rui Peng and Feng Zhou",

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year = "2020",

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doi = "10.1007/s11425-018-9447-y",

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T1 - Nonexistence of positive supersolutions to a class of semilinear elliptic equations and systems in an exterior domain

AU - Chen, Huyuan

AU - Peng, Rui

AU - Zhou, Feng

PY - 2020/7/1

Y1 - 2020/7/1

N2 - In this paper, we consider the following semilinear elliptic equation: {−Δu=h(x,u)inΩ,u⩾0on∂Ω, where Ω is an exterior domain in ℝN with N ⩾ 3, h: Ω × ℝ+ → ℝ is a measurable function, and derive optimal nonexistence results of positive supersolutions. Our argument is based on a nonexistence result of positive supersolutions of a linear elliptic problem with Hardy potential. We also establish sharp nonexistence results of positive supersolutions to an elliptic system.

AB - In this paper, we consider the following semilinear elliptic equation: {−Δu=h(x,u)inΩ,u⩾0on∂Ω, where Ω is an exterior domain in ℝN with N ⩾ 3, h: Ω × ℝ+ → ℝ is a measurable function, and derive optimal nonexistence results of positive supersolutions. Our argument is based on a nonexistence result of positive supersolutions of a linear elliptic problem with Hardy potential. We also establish sharp nonexistence results of positive supersolutions to an elliptic system.

KW - 35B53

KW - 35J60

KW - nonexistence

KW - semilinear elliptic problem

KW - supersolution

UR - https://www.scopus.com/pages/publications/85068312189

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DO - 10.1007/s11425-018-9447-y

M3 - 文章

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SN - 1674-7283

VL - 63

SP - 1307

EP - 1322

JO - Science China Mathematics

JF - Science China Mathematics

IS - 7

ER -

Nonexistence of positive supersolutions to a class of semilinear elliptic equations and systems in an exterior domain

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