[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 WeidongShan 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 Schrödinger 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:

[1]LASKIN N. Fractional quantum mechanics and path integrals[J]. Physics letters,2000,A 269:298-305.
[2]AMBROSIO V,HAJAIEJ H. Multiple solutions for a class of nonhomogeneous fractional Schrödinger equations in RN[J]. Journal of dynamics and differential equations,2018,30:1119-1143.
[3]CHANG X. Ground state solutions of asymptotically linear fractional Schrödinger equation[J]. Journal of mathematical physics,2013,54:061504.
[4]CHANG X,WANG Z Q. Ground state of scalar field equations involving a fractional Laplacian with general nonlinearity[J]. Nonlinearity,2013,26:479-494.
[5]FELMER P,QUAAS A,TAN J. Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian[J]. Proceedings of the Royal Society A,2012,142:1237-1262.
[6]LIU Z,LUO H,ZHANG Z. Dancer-Fucik spectrum for fractional Schrödinger operators with a steep potential well on RN[J]. Nonlinear analysis,2019,189:1-26.
[7]SECCHI S. Ground state solutions for nonlinear fractional Schrödinger equations in RN[J]. Nonlinear analysis,2019,189:1-26.
[7]SECCHI S. Ground state solutions for nonlinear fractional Schrödinger equations in . Journal of mathematical physics,2013,54:031501.
[8]WAN Y,WANG Z. Bound state for fractional Schrödinger equation with saturable nonlinearity[J]. Applied mathematics and computation,2016,273:735-740.
[9]YANG L,LIU Z. Multiplicity and concentration of solutions for fractional Schrödinger equation with sublinear perturbation and steep potential well[J]. Computers and mathematics with applications,2016,72:1629-1640.
[10]BARTSCH T,PANKOV A,WANG Z Q. Nonlinear schrödinger equations with steep potential well[J]. Communications in contemporary mathematics,2001,3:549-569.
[11]HEERDEN F A. Multiple solutions for a Schrödinger type equation with an asymptotically linear term[J]. Nonlinear analysis,2003,55:739-758.
[12]LIU Z L,HEERDEN F A,WANG Z Q. Nodal type bound states of Schrödinger equations via invariant set and minimax methods[J]. Journal of differential equations,2005,214:358-390.
[13]JIANG Y,ZHOU H. Schrödinger-Poisson system with steep potential well[J]. Journal of differential equations,2011,251:582-608.
[14]ZHAO L,LIU H,ZHAO F. Existence and concentration of solutions for the Schrödinger-Poisson equations with steep potential well[J]. Journal of differential equations,2013,255:1-23.
[15]SUN J,WU T. Ground state solutions for an indefinite Krichhoff type problem with steep potential[J]. Journal of differential equations,2015,256:1771-1792.
[16]SERVADEI R,VALDINOCI E. Variational methods for non-local operators of elliptic type[J]. Discrete continuous dynamical systems,2013,33:2105-2137.
[17]ZHAO F,ZHAO L,DING Y. Existence and multiplicity of solutions for a non-periodic Schrödinger equation[J]. Nonlinear analysis,2008,69:3671-3678.
[18]STRUWE M. Variational methods:applications to nonlinear partial differential equations and hamiltonian systems[M]. Fourth Edition. Springer,Berlin,New York,2008.

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