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

页码：123 / 150

页数：28

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