Existence of ground state solutions to some Nonlinear Schrodinger equations on lattice graphs

被引：9
|
作者：
Hua, Bobo [1 ,2 ]
Xu, Wendi [3 ]
机构：
[1] Fudan Univ, Sch Math Sci, LMNS, Shanghai 200433, Peoples R China
[2] Fudan Univ, Shanghai Ctr Math Sci, Jiangwan Campus,2005 Songhu Rd, Shanghai 200438, Peoples R China
[3] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
来源：
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 62卷 / 04期
关键词：
35Q55; 39A14; 58E30;
D O I：
10.1007/s00526-023-02470-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the nonlinear Schrodinger equation -?u + V (x)u = f (x, u) on the lattice graph Z(N). Using the Nehari method, we prove that when f satisfies some growth conditions and the potential function V is periodic or bounded, the above equation admits a ground state solution. Moreover, we extend our results from Z(N) to quasi-transitive graphs.
引用
收藏
页数：17
相关论文
共 50 条
  • [1] Existence of ground state solutions to some Nonlinear Schrödinger equations on lattice graphs
    Bobo Hua
    Wendi Xu
    Calculus of Variations and Partial Differential Equations, 2023, 62
  • [2] Convergence of ground state solutions for nonlinear Schrodinger equations on graphs
    Zhang, Ning
    Zhao, Liang
    SCIENCE CHINA-MATHEMATICS, 2018, 61 (08) : 1481 - 1494
  • [3] Existence and Concentration of Ground State Solutions for the Coupled Nonlinear Schrodinger Equations
    Wang, Wenbo
    Li, Quanqing
    Zhou, Jianwen
    Li, Yongkun
    SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2021, 45 (04) : 533 - 560
  • [4] On the Existence of Ground State Solutions of the Periodic Discrete Coupled Nonlinear Schrodinger Lattice
    Huang, Meihua
    Zhou, Zhan
    JOURNAL OF APPLIED MATHEMATICS, 2013,
  • [5] Existence and nonexistence of the ground state solutions for nonlinear Schrodinger equations with nonperiodic nonlinearities
    Wang, Jun
    Tian, Lixin
    Xu, Junxiang
    Zhang, Fubao
    MATHEMATISCHE NACHRICHTEN, 2012, 285 (11-12) : 1543 - 1562
  • [6] On the notion of ground state for nonlinear Schrodinger equations on metric graphs
    De Coster, Colette
    Dovetta, Simone
    Galant, Damien
    Serra, Enrico
    CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2023, 62 (05)
  • [7] EXISTENCE OF SOLUTIONS OF NONLINEAR SCHRODINGER EQUATIONS
    SCHMITT, K
    TSAI, L
    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1977, 76 : 227 - 232
  • [8] Ground state solutions for the nonlinear Schrodinger-Maxwell equations
    Azzollini, A.
    Pomponio, A.
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 345 (01) : 90 - 108
  • [9] Ground state solutions for nonlinear fractional Schrodinger equations in RN
    Secchi, Simone
    JOURNAL OF MATHEMATICAL PHYSICS, 2013, 54 (03)
  • [10] Ground state solutions for periodic Discrete nonlinear Schrodinger equations
    Xu, Xionghui
    Sun, Jijiang
    AIMS MATHEMATICS, 2021, 6 (12): : 13057 - 13071
12345