[1]陆伟东,单 远.带有位势井的分数阶渐近薛定谔方程的多解性研究[J].南京师大学报(自然科学版),2023,46(01):1-5.[doi:10.3969/j.issn.1001-4616.2023.01.001]
　Lu Weidong,Shan Yuan.Multiple Solutions for Asymptotically Linear Fractional Schrdinger Equation with Steep Potential Well[J].Journal of Nanjing Normal University(Natural Science Edition),2023,46(01):1-5.[doi:10.3969/j.issn.1001-4616.2023.01.001]
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带有位势井的分数阶渐近薛定谔方程的多解性研究()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第46卷
期数:
2023年01期
页码:
1-5
栏目:
数学
出版日期:
2023-03-15

文章信息/Info

Title:
Multiple Solutions for Asymptotically Linear Fractional Schrödinger Equation with Steep Potential Well
文章编号:
1001-4616(2023)01-0001-05
作者:
陆伟东; 单 远
(南京审计大学数学学院，江苏 南京 211815)
Author(s):
Lu Weidong; Shan Yuan
(School of Mathematics of Nanjing Audit University, Nanjing 211815, China)
关键词:
分数阶薛定谔方程; 位势井; 渐近线性条件; 多解性
Keywords:
fractional Schrö; dinger equation;  steep potential well;  asymptotically linear condition;  multiple solutions
分类号:
O177.91
DOI:
10.3969/j.issn.1001-4616.2023.01.001
文献标志码:
A
摘要:
研究分数阶薛定谔方程:(-Δ)su+Vλ(x)u=f(x,u), 0<s<1, x∈RN,其中N>2s,f满足渐近线性条件,且当λ充分大时位势函数Vλ具有位势井. 利用临界点定理得到方程的多解性.
Abstract:
In this paper, we study the nonlinear fractional Schrödinger equation (-Δ)su+Vλ(x)u=f(x,u), 0<s<1, x∈RN, on the whole space RN with N>2s. The nonlinearity f is assumed to be asymptotically linear and the potential Vλ has a steep potential well for sufficiently large parameter λ. By virtue of critical point theory, the existence of multiple solutions are obtained.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2022-09-23.
基金项目:国家自然科学基金项目(11971233).
通讯作者:单远,副教授,研究方向:微分动力系统. E-mail:shannjnu@gmail.com
更新日期/Last Update: 2023-03-15