Property of solutions for elliptic equation involving the higher-order fractional laplacian in Rn+

Mei Yu; Xia Zhang; Binlin Zhang

doi:10.3934/cpaa.2020157

Property of solutions for elliptic equation involving the higher-order fractional laplacian in Rn+

Mei Yu
, Xia Zhang
, Binlin Zhang^*

^*Corresponding author for this work

School of Mathematics

Northwestern Polytechnical University Xian
Yeshiva University
Shandong University of Science and Technology

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

1 Scopus citations

Abstract

In this paper, we consider the following equation with the higher-order fractional Laplacian (-Δ)s for s = m + α 2 : (Equation Presented) where m ∈ N∗, 0 < α < 2. By developing a narrow region principle in un-bounded domain and establishing a equivalence of differential equation and integral equation, together with the method of moving planes, we deduce the monotonicity property of positive solutions and the Liouville theorem of non- negative solutions.

Original language	English
Pages (from-to)	3597-3612
Number of pages	16
Journal	Communications on Pure and Applied Analysis
Volume	19
Issue number	7
DOIs	https://doi.org/10.3934/cpaa.2020157
State	Published - Jul 2020

Keywords

Higher-order fractional Laplacian
Liouville theorem
Method of moving planes
Monotonicity

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title = "Property of solutions for elliptic equation involving the higher-order fractional laplacian in Rn+",

abstract = "In this paper, we consider the following equation with the higher-order fractional Laplacian (-Δ)s for s = m + α 2 : (Equation Presented) where m ∈ N∗, 0 < α < 2. By developing a narrow region principle in un-bounded domain and establishing a equivalence of differential equation and integral equation, together with the method of moving planes, we deduce the monotonicity property of positive solutions and the Liouville theorem of non- negative solutions.",

keywords = "Higher-order fractional Laplacian, Liouville theorem, Method of moving planes, Monotonicity",

author = "Mei Yu and Xia Zhang and Binlin Zhang",

year = "2020",

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doi = "10.3934/cpaa.2020157",

language = "英语",

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journal = "Communications on Pure and Applied Analysis",

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T1 - Property of solutions for elliptic equation involving the higher-order fractional laplacian in Rn+

AU - Yu, Mei

AU - Zhang, Xia

AU - Zhang, Binlin

PY - 2020/7

Y1 - 2020/7

N2 - In this paper, we consider the following equation with the higher-order fractional Laplacian (-Δ)s for s = m + α 2 : (Equation Presented) where m ∈ N∗, 0 < α < 2. By developing a narrow region principle in un-bounded domain and establishing a equivalence of differential equation and integral equation, together with the method of moving planes, we deduce the monotonicity property of positive solutions and the Liouville theorem of non- negative solutions.

AB - In this paper, we consider the following equation with the higher-order fractional Laplacian (-Δ)s for s = m + α 2 : (Equation Presented) where m ∈ N∗, 0 < α < 2. By developing a narrow region principle in un-bounded domain and establishing a equivalence of differential equation and integral equation, together with the method of moving planes, we deduce the monotonicity property of positive solutions and the Liouville theorem of non- negative solutions.

KW - Higher-order fractional Laplacian

KW - Liouville theorem

KW - Method of moving planes

KW - Monotonicity

UR - https://www.scopus.com/pages/publications/85090892088

U2 - 10.3934/cpaa.2020157

DO - 10.3934/cpaa.2020157

M3 - 文章

AN - SCOPUS:85090892088

SN - 1534-0392

VL - 19

SP - 3597

EP - 3612

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 7

ER -

Property of solutions for elliptic equation involving the higher-order fractional laplacian in Rn+

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Keywords

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