ON A SUPER POLYHARMONIC PROPERTY OF A HIGHER-ORDER FRACTIONAL LAPLACIAN

被引：0
作者：
徐美清
机构：
[1] SchoolofMathematicalScience,ShanghaiJiaoTongUniversity
来源：
ActaMathematicaScientia | 2023年 / 43卷 / 06期
关键词：
D O I：
暂无
中图分类号：
O177 [泛函分析];
学科分类号：
070104 ;
摘要：
Let 0 1,m ∈N+.Consider the positive solution u of the PDE（-Δ） α/2+m u（x）=up（x） in R~n.（0.1）In [1]（Transactions of the American Mathematical Society,2021）,Cao,Dai and Qin showed that,under the condition u ∈Lα,（0.1） possesses a super poly harmonic property（-Δ）k+α/2 u≥0 for k=0,1,…,m-1.In this paper,we show another kind of super poly harmonic property（-Δ）ku> 0 for k=1,…,m-1,under the conditions（-Δ）mu ∈Lα and（-Δ）mu≥ 0.Both kinds of super polyharmonic properties can lead to an equivalence between（0.1） and the integral equation u（x）=∫R~nup（y）/(|x-y|n-2m-α)dy.One can classify solutions to（0.1） following the work of [2] and [3] by Chen,Li,Ou.
引用
收藏
页码：2589 / 2596
页数：8
相关论文
共 24 条
[1]  
Classification of anti-symmetric solutions to nonlinear fractional Laplace equations[J] Zhuo Ran;Li Congming Calculus of Variations and Partial Differential Equations 2021,
[2]  
Super poly-harmonic properties; Liouville theorems and classification of nonnegative solutions to equations involving higher-order fractional Laplacians[J] Daomin Cao;Wei Dai;Guolin Qin Transactions of the American Mathematical Society 2021,
[3]  
Non-negative solutions to fractional Laplace equations with isolated singularity[J] Congming Li;Chenkai Liu;Zhigang Wu;Hao Xu Advances in Mathematics 2020,
[4]  
A Liouville theorem for the higher-order fractional Laplacian[J] Ran Zhuo;Yan Li Communications in Contemporary Mathematics 2019,
[5]  
A direct method of moving planes for the system of the fractional Laplacian[J] Chunxia Cheng;Zhongxue Lü;Yingshu Lü Pacific Journal of Mathematics 2017,
[6]  
A direct method of moving planes for the fractional Laplacian[J] Wenxiong Chen;Congming Li;Yan Li Advances in Mathematics 2017,
[7]  
A Liouville type theorem for higher order Hardy–Hénon equation in R n[J] Tingzhi Cheng;Shuang Liu Journal of Mathematical Analysis and Applications 2016,
[8]  
SOME OBSERVATIONS ON THE GREEN FUNCTION FOR THE BALL IN THE FRACTIONAL LAPLACE FRAMEWORK[J] Claudia Bucur Communications on Pure & Applied Analysis 2016,
[9]  
Super poly-harmonic property of solutions for Navier boundary problems on a half space[J] SPINELLA MARCELLO Journal of Functional Analysis 2013,
[10]  
SUPER POLYHARMONIC PROPERTY OF SOLUTIONS FOR PDE SYSTEMS AND ITS APPLICATIONS[J] Wenxiong Chen;CONGMING Li Communications on pure and applied analysis 2013,
123