POSITIVE EIGENFUNCTIONS OF A CLASS OF FRACTIONAL SCHRODINGER OPERATOR WITH A POTENTIAL WELL

被引：0
|
作者：
Gu, Guangze [1 ]
Yang, Zhipeng [2 ,3 ]
机构：
[1] Yunnan Normal Univ, Dept Math, Kunming 650500, Yunnan, Peoples R China
[2] Harbin Normal Univ, Sch Math Sci, Harbin 150025, Peoples R China
[3] Georg August Univ Gottingen, Math Inst, D-37073 Gottingen, Germany
来源：
DIFFERENTIAL AND INTEGRAL EQUATIONS | 2022年 / 35卷 / 1-2期
基金：
中国国家自然科学基金;
关键词：
OBSTACLE PROBLEM; EQUATION; REGULARITY; UNIQUENESS; BOUNDARY; BEHAVIOR;
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 are concerned with the following eigenvalue problem (-Delta)(s) u + lambda g(x) u = alpha u, u is an element of H-s (R-N), N >= 3, where s is an element of (0,1), alpha, lambda is an element of R and g(x) 0 on (Omega) over bar, g (x) is an element of (0, 1] on R-N\(Omega) over bar and lim(vertical bar x vertical bar ->infinity) g (x) = 1 for some bounded open set Omega subset of R-N. We discuss the existence and some properties of the first two eigenvalues for this problem, which extend some classical results for semilinear Schrodinger equations to the nonlocal fractional setting.
引用
收藏
页码：123 / 150
页数：28
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