QUALITATIVE PROPERTIES OF POSITIVE SOLUTIONS OF A MIXED ORDER NONLINEAR SCHRODINGER EQUATION

被引：0

作者：

Dipierro, Serena ^{[1
]}

Su, Xifeng ^{[2
]}

Valdinoci, Enrico ^{[1
]}

Zhang, Jiwen ^{[2
]}

机构：

[1] Univ Western Australia, Dept Math & Stat, 35 Stirling Highway, Crawley, WA 6009, Australia

[2] Beijing Normal Univ, Sch Math Sci, 19 XinJieKouWai St, Beijing 100875, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2025年 / 45卷 / 06期

基金：

澳大利亚研究理事会; 中国国家自然科学基金;

关键词：

Mixed order operators; regularity theory; power-type decay; heat kernel; HARNACK INEQUALITY; RADIAL SOLUTIONS; UNIQUENESS; DELTA-U+F(U)=0; STATES;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we deal with the mixed local/nonlo cal Schroddinger equation { -Delta u + (-Delta)(s)u + u = u(p) in R-n , u > 0 in R-n , lim(|x|->+infinity) u ( x ) = 0, where n >= 2, s is an element of (0, 1), and p is an element of (1, n +2 / n - 2) The existence of positive solutions for the above problem is proved, relying on some new regularity results. In addition, we study the power-type decay and the radial symmetry properties of such solutions. The methods also make use of some basic properties of the heat kernel and the Bessel kernel associated with the operator -Delta + (-Delta)(s). In this context, we provide self-contained proofs of these results based on Fourier analysis techniques.

引用

页码：1948 / 2000

页数：53

共 33 条

[31] Regularity results for solutions of mixed local and nonlocal elliptic equations
Su, Xifeng
Valdinoci, Enrico
Wei, Yuanhong
Zhang, Jiwen
[J]. MATHEMATISCHE ZEITSCHRIFT, 2022, 302 (03) : 1855 - 1878
[32] ON CONCENTRATION OF POSITIVE BOUND-STATES OF NONLINEAR SCHRODINGER-EQUATIONS
WANG, XF
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1993, 153 (02) : 229 - 244
[33] ZELATI VC, 1992, COMMUN PUR APPL MATH, V45, P1217

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