On a weighted semilinear Steklov problem in exterior domains

Zongming Guo; Fangshu Wan; Dong Ye

doi:10.1016/j.jde.2025.113608

On a weighted semilinear Steklov problem in exterior domains

Zongming Guo
, Fangshu Wan
, Dong Ye^*

^*Corresponding author for this work

School of Mathematical Sciences

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

Abstract

Let B be the unit ball in R^N, N≥3. We are interested in a weighted elliptic problem in R^N﹨B‾ with Steklov boundary conditions: [Formula presented] with d∈R, p>1 and N^′:=N+θ>2,τ:=ℓ−θ>−2. A complete picture of existence and nonexistence of radial solutions for (0.1) is obtained. Furthermore, for d<0, the asymptotic behavior of radial solutions to (0.1) as p→∞ is studied.

Original language	English
Article number	113608
Journal	Journal of Differential Equations
Volume	446
DOIs	https://doi.org/10.1016/j.jde.2025.113608
State	Published - 25 Nov 2025

Keywords

Asymptotic behavior
Existence and nonexistence
Exterior domains
Positive radial solutions
Steklov boundary value problem

Access to Document

10.1016/j.jde.2025.113608

Cite this

@article{cdb41be33e864f6a98f36dc1ebb92e7b,

title = "On a weighted semilinear Steklov problem in exterior domains",

abstract = "Let B be the unit ball in RN, N≥3. We are interested in a weighted elliptic problem in RN﹨B‾ with Steklov boundary conditions: [Formula presented] with d∈R, p>1 and N′:=N+θ>2,τ:=ℓ−θ>−2. A complete picture of existence and nonexistence of radial solutions for (0.1) is obtained. Furthermore, for d<0, the asymptotic behavior of radial solutions to (0.1) as p→∞ is studied.",

keywords = "Asymptotic behavior, Existence and nonexistence, Exterior domains, Positive radial solutions, Steklov boundary value problem",

author = "Zongming Guo and Fangshu Wan and Dong Ye",

note = "Publisher Copyright: {\textcopyright} 2025 Elsevier Inc.",

year = "2025",

month = nov,

day = "25",

doi = "10.1016/j.jde.2025.113608",

language = "英语",

volume = "446",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - On a weighted semilinear Steklov problem in exterior domains

AU - Guo, Zongming

AU - Wan, Fangshu

AU - Ye, Dong

PY - 2025/11/25

Y1 - 2025/11/25

N2 - Let B be the unit ball in RN, N≥3. We are interested in a weighted elliptic problem in RN﹨B‾ with Steklov boundary conditions: [Formula presented] with d∈R, p>1 and N′:=N+θ>2,τ:=ℓ−θ>−2. A complete picture of existence and nonexistence of radial solutions for (0.1) is obtained. Furthermore, for d<0, the asymptotic behavior of radial solutions to (0.1) as p→∞ is studied.

AB - Let B be the unit ball in RN, N≥3. We are interested in a weighted elliptic problem in RN﹨B‾ with Steklov boundary conditions: [Formula presented] with d∈R, p>1 and N′:=N+θ>2,τ:=ℓ−θ>−2. A complete picture of existence and nonexistence of radial solutions for (0.1) is obtained. Furthermore, for d<0, the asymptotic behavior of radial solutions to (0.1) as p→∞ is studied.

KW - Asymptotic behavior

KW - Existence and nonexistence

KW - Exterior domains

KW - Positive radial solutions

KW - Steklov boundary value problem

UR - https://www.scopus.com/pages/publications/105010628874

U2 - 10.1016/j.jde.2025.113608

DO - 10.1016/j.jde.2025.113608

M3 - 文章

AN - SCOPUS:105010628874

SN - 0022-0396

VL - 446

JO - Journal of Differential Equations

JF - Journal of Differential Equations

M1 - 113608

ER -

On a weighted semilinear Steklov problem in exterior domains

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this