Symmetry and monotonicity of nonnegative solutions to pseudo-relativistic Choquard equations

Yuxia Guo; Shaolong Peng

doi:10.1007/s00033-021-01551-5

Symmetry and monotonicity of nonnegative solutions to pseudo-relativistic Choquard equations

Yuxia Guo^*
, Shaolong Peng

^*Corresponding author for this work

Tsinghua University

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

20 Scopus citations

Abstract

In this paper, we consider the following pseudo-relativistic Choquard equations: (-Δ+m2)su+wu=RN,t(1|x-y|N-2t∗up)uq,inRN,where s, t∈ (0 , 1) , mass m> 0 , w> - m²^s, 2 < p< ∞, and 0 < q≤ p- 1. We first establish a narrow region principle for pseudo-relativistic Choquard equations and estimate the decay of the solutions at infinity. Using the generalized direct method of moving planes, we obtain the radial symmetry and monotonicity of nonnegative solutions for the above equations.

Original language	English
Article number	120
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	72
Issue number	3
DOIs	https://doi.org/10.1007/s00033-021-01551-5
State	Published - Jun 2021
Externally published	Yes

Keywords

Generalized direct method of moving planes
Narrow region principle
Pseudo-relativistic Choquard equations

Access to Document

10.1007/s00033-021-01551-5

Cite this

@article{678eb60ec8f341b68aa03d0720f994a2,

title = "Symmetry and monotonicity of nonnegative solutions to pseudo-relativistic Choquard equations",

abstract = "In this paper, we consider the following pseudo-relativistic Choquard equations: (-Δ+m2)su+wu=RN,t(1|x-y|N-2t∗up)uq,inRN,where s, t∈ (0 , 1) , mass m> 0 , w> - m2s, 2 < p< ∞, and 0 < q≤ p- 1. We first establish a narrow region principle for pseudo-relativistic Choquard equations and estimate the decay of the solutions at infinity. Using the generalized direct method of moving planes, we obtain the radial symmetry and monotonicity of nonnegative solutions for the above equations.",

keywords = "Generalized direct method of moving planes, Narrow region principle, Pseudo-relativistic Choquard equations",

author = "Yuxia Guo and Shaolong Peng",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2021",

month = jun,

doi = "10.1007/s00033-021-01551-5",

language = "英语",

volume = "72",

journal = "Zeitschrift fur Angewandte Mathematik und Physik",

issn = "0044-2275",

publisher = "Birkhauser Verlag Basel",

number = "3",

}

TY - JOUR

T1 - Symmetry and monotonicity of nonnegative solutions to pseudo-relativistic Choquard equations

AU - Guo, Yuxia

AU - Peng, Shaolong

PY - 2021/6

Y1 - 2021/6

N2 - In this paper, we consider the following pseudo-relativistic Choquard equations: (-Δ+m2)su+wu=RN,t(1|x-y|N-2t∗up)uq,inRN,where s, t∈ (0 , 1) , mass m> 0 , w> - m2s, 2 < p< ∞, and 0 < q≤ p- 1. We first establish a narrow region principle for pseudo-relativistic Choquard equations and estimate the decay of the solutions at infinity. Using the generalized direct method of moving planes, we obtain the radial symmetry and monotonicity of nonnegative solutions for the above equations.

AB - In this paper, we consider the following pseudo-relativistic Choquard equations: (-Δ+m2)su+wu=RN,t(1|x-y|N-2t∗up)uq,inRN,where s, t∈ (0 , 1) , mass m> 0 , w> - m2s, 2 < p< ∞, and 0 < q≤ p- 1. We first establish a narrow region principle for pseudo-relativistic Choquard equations and estimate the decay of the solutions at infinity. Using the generalized direct method of moving planes, we obtain the radial symmetry and monotonicity of nonnegative solutions for the above equations.

KW - Generalized direct method of moving planes

KW - Narrow region principle

KW - Pseudo-relativistic Choquard equations

UR - https://www.scopus.com/pages/publications/85105986702

U2 - 10.1007/s00033-021-01551-5

DO - 10.1007/s00033-021-01551-5

M3 - 文章

AN - SCOPUS:85105986702

SN - 0044-2275

VL - 72

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

IS - 3

M1 - 120

ER -

Symmetry and monotonicity of nonnegative solutions to pseudo-relativistic Choquard equations

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this