Multiplicity and concentration of positive solutions for the fractional Schrödinger–Poisson systems with critical growth
ESAIM: COCV, 23 4 (2017) 1515-1542
Published online: 2017-08-08
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Positive Bound States of Fractional Schrödinger–Poisson System with Doubly Critical Exponents in Exterior Domains
Da-Bin Wang, Huafei Xie and Huabo ZhangThe Journal of Geometric Analysis 35 (4) (2025)
https://doi.org/10.1007/s12220-025-01954-0
Multi-bump Solutions for a Logarithmic Fractional Schrödinger-Poisson System with Deepening Potential Well
Lin Li and Huo TaoThe Journal of Geometric Analysis 35 (6) (2025)
https://doi.org/10.1007/s12220-025-02014-3
Multiple solutions for a class of Kirchhoff-type equation with critical growth
Yiwei Ye and Shan LiuElectronic Journal of Qualitative Theory of Differential Equations (7) 1 (2025)
https://doi.org/10.14232/ejqtde.2025.1.7
Ground states of the inhomogeneous nonlinear fractional Schrödinger-Poisson equations
Ming Cheng and Kunhui ShaoComplex Variables and Elliptic Equations 1 (2025)
https://doi.org/10.1080/17476933.2024.2439963
Multiplicity of positive solutions for the fractional Schrödinger–Poisson system with critical nonlocal term
Xilin Dou, Xiaoming He and Vicenţiu D. RădulescuBulletin of Mathematical Sciences 14 (02) (2024)
https://doi.org/10.1142/S1664360723500121
On the existence of solutions for a class of nonlinear fractional Schrödinger-Poisson system: Subcritical and critical cases
Lin Li, Huo Tao and Stepan TersianFractional Calculus and Applied Analysis 27 (4) 1670 (2024)
https://doi.org/10.1007/s13540-024-00296-y
Multiple bound states for a class of fractional critical Schrödinger–Poisson systems with critical frequency
Xiaoming He, Yuxi Meng and Patrick WinkertJournal of Mathematical Physics 65 (7) (2024)
https://doi.org/10.1063/5.0174872
Multiplicity of Normalized Solutions for the Fractional Schrödinger Equation with Potentials
Xue Zhang, Marco Squassina and Jianjun ZhangMathematics 12 (5) 772 (2024)
https://doi.org/10.3390/math12050772
Critical fractional Schrödinger-Poisson systems with lower perturbations: the existence and concentration behavior of ground state solutions
Shenghao Feng, Jianhua Chen and Xianjiu HuangAdvances in Nonlinear Analysis 13 (1) (2024)
https://doi.org/10.1515/anona-2024-0006
On the logarithmic fractional Schrödinger–Poisson system with saddle-like potential
Huo Tao and Lin LiElectronic Journal of Qualitative Theory of Differential Equations (36) 1 (2024)
https://doi.org/10.14232/ejqtde.2024.1.36
Existence of Nontrivial Solution for a Class of Fractional Schro¨dinger-Poisson System
娟霞 孟Advances in Applied Mathematics 12 (04) 1704 (2023)
https://doi.org/10.12677/AAM.2023.124177
Fractional Schrödinger–Poisson system with critical growth and potentials vanishing at infinity
Xinrui Zhang and Xiaoming HeMathematische Nachrichten 296 (5) 2167 (2023)
https://doi.org/10.1002/mana.202100094
Multiple Positive Bound State Solutions for Fractional Schrödinger–Poisson System with Critical Nonlocal Term
Xiaoming He and Da-Bin WangThe Journal of Geometric Analysis 33 (6) (2023)
https://doi.org/10.1007/s12220-023-01247-4
On the eigenvalue problem of Schrödinger-Poisson system
Zhisu LiuProceedings of the American Mathematical Society 151 (7) 3059 (2023)
https://doi.org/10.1090/proc/16366
Multiplicity and concentration of solutions for a class of magnetic Schrödinger–Poisson system with double critical growths
Xiaolu Lin and Shenzhou ZhengZeitschrift für angewandte Mathematik und Physik 74 (3) (2023)
https://doi.org/10.1007/s00033-023-01991-1
On a Fractional Schrödinger–Poisson System with Doubly Critical Growth and a Steep Potential Well
Jiali Lan and Xiaoming HeThe Journal of Geometric Analysis 33 (6) (2023)
https://doi.org/10.1007/s12220-023-01238-5
On a class of fractional Kirchhoff–Schrödinger–Poisson systems involving magnetic fields
Xiaolu Lin and Shenzhou ZhengCommunications in Nonlinear Science and Numerical Simulation 124 107312 (2023)
https://doi.org/10.1016/j.cnsns.2023.107312
Multiple Positive Solutions for Fractional Schrödinger–Poisson System with Doubly Critical Exponents
Wei Jiang and Jia-Feng LiaoQualitative Theory of Dynamical Systems 22 (1) (2023)
https://doi.org/10.1007/s12346-022-00726-3
Multiplicity and concentration of solutions for a fractional Schrödinger–Poisson system with sign-changing potential
Guofeng Che and Haibo ChenApplicable Analysis 102 (1) 253 (2023)
https://doi.org/10.1080/00036811.2021.1950692
Ground‐state solution of a nonlinear fractional Schrödinger–Poisson system
Haidong Liu and Leiga ZhaoMathematical Methods in the Applied Sciences 45 (4) 1934 (2022)
https://doi.org/10.1002/mma.7899
Existence and Concentration of Solutions for the Sublinear Fractional Schrödinger–Poisson System
Guofeng Che and Haibo ChenBulletin of the Malaysian Mathematical Sciences Society 45 (6) 2843 (2022)
https://doi.org/10.1007/s40840-022-01294-0
Ground states for critical fractional Schrödinger‐Poisson systems with vanishing potentials
Xilin Dou and Xiaoming HeMathematical Methods in the Applied Sciences 45 (16) 9089 (2022)
https://doi.org/10.1002/mma.8294
Concentration of solutions for fractional Kirchhoff equations with discontinuous reaction
Zhisu Liu, Vicenţiu D. Rădulescu and Ziqing YuanZeitschrift für angewandte Mathematik und Physik 73 (5) (2022)
https://doi.org/10.1007/s00033-022-01849-y
Concentration of bound states for fractional Schrödinger-Poisson system via penalization methods
Kaimin Teng and Xian WuCommunications on Pure & Applied Analysis 21 (4) 1157 (2022)
https://doi.org/10.3934/cpaa.2022014
Multiplicity of high energy solutions for fractional Schrodinger-Poisson systems with critical frequency
Siqi Qu and Xiaoming HeElectronic Journal of Differential Equations 2022 (01-87) 47 (2022)
https://doi.org/10.58997/ejde.2022.47
On the number of concentrating solutions of a fractional Schrödinger–Poisson system with doubly critical growth
Siqi Qu and Xiaoming HeAnalysis and Mathematical Physics 12 (2) (2022)
https://doi.org/10.1007/s13324-022-00675-9
Ground state solutions for a class of fractional Schrodinger-Poisson system with critical growth and vanishing potentials
Yuxi Meng, Xinrui Zhang and Xiaoming HeAdvances in Nonlinear Analysis 10 (1) 1328 (2021)
https://doi.org/10.1515/anona-2020-0179
The nontrivial solutions for fractional Schrödinger–Poisson equations with magnetic fields and critical or supercritical growth
Lintao Liu and Haibo ChenApplied Mathematics Letters 121 107358 (2021)
https://doi.org/10.1016/j.aml.2021.107358
On the asymptotically cubic fractional Schrödinger–Poisson system
Wenbo Wang, Yuanyang Yu and Yongkun LiApplicable Analysis 100 (4) 695 (2021)
https://doi.org/10.1080/00036811.2019.1616695
Bound states for fractional Schrödinger-Poisson system with critical exponent
Mengyao Chen, Qi Li and Shuangjie PengDiscrete & Continuous Dynamical Systems - S 14 (6) 1819 (2021)
https://doi.org/10.3934/dcdss.2021038
Nonlinear Fractional Schrödinger Equations in R^N
Vincenzo AmbrosioFrontiers in Mathematics, Nonlinear Fractional Schrödinger Equations in R^N 443 (2021)
https://doi.org/10.1007/978-3-030-60220-8_13
Infinitely many solutions for a class of sublinear fractional Schrödinger-Poisson systems
Wen Guan, Lu-Ping Ma, Da-Bin Wang and Jin-Long ZhangQuaestiones Mathematicae 44 (9) 1197 (2021)
https://doi.org/10.2989/16073606.2020.1781282
Ground state and multiple solutions for critical fractional Schrodinger-Poisson equations with perturbation terms
Lintao Liu and Kaimin TengElectronic Journal of Differential Equations 2021 (01-104) 07 (2021)
https://doi.org/10.58997/ejde.2021.07
Existence and concentration results for fractional Schrodinger-Poisson system via penalization method
Zhipeng Yang, Wei Zhang and Fukun ZhaoElectronic Journal of Differential Equations 2021 (01-104) 14 (2021)
https://doi.org/10.58997/ejde.2021.14
Multiple solutions for a Choquard system with periodic potential
Long-Jiang GuJournal of Mathematical Analysis and Applications 484 (1) 123704 (2020)
https://doi.org/10.1016/j.jmaa.2019.123704
Multiplicity and Concentration Results for Fractional Schrödinger-Poisson Equations with Magnetic Fields and Critical Growth
Vincenzo AmbrosioPotential Analysis 52 (4) 565 (2020)
https://doi.org/10.1007/s11118-018-9751-1
EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR $P(X)$-LAPLACIAN DIFFERENTIAL INCLUSIONS INVOLVING CRITICAL GROWTH
Ziqing Yuan and Mugen HuangJournal of Applied Analysis & Computation 10 (4) 1416 (2020)
https://doi.org/10.11948/20190216
Ground state solutions of Nehari-Pohozaev type for a fractional Schrödinger-Poisson system with critical growth
Wentao Huang and Li WangActa Mathematica Scientia 40 (4) 1064 (2020)
https://doi.org/10.1007/s10473-020-0413-1
Ground state solutions for the periodic fractional Schrödinger–Poisson systems with critical Sobolev exponent
Mingzhu Yu, Haibo Chen and Weihong XieRocky Mountain Journal of Mathematics 50 (2) (2020)
https://doi.org/10.1216/rmj.2020.50.719
Multiplicity and concentration results for a class of critical fractional Schrödinger–Poisson systems via penalization method
Vincenzo AmbrosioCommunications in Contemporary Mathematics 22 (01) 1850078 (2020)
https://doi.org/10.1142/S0219199718500785
Ground state and sign-changing solutions for fractional Schrödinger–Poisson system with critical growth
Chaoxia Ye and Kaimin TengComplex Variables and Elliptic Equations 65 (8) 1360 (2020)
https://doi.org/10.1080/17476933.2019.1652278
Nontrivial solutions for the fractional Schrödinger‐Poisson system with subcritical or critical nonlinearities
Zi‐an FanMathematical Methods in the Applied Sciences 43 (3) 1484 (2020)
https://doi.org/10.1002/mma.6019
Existence of solutions for Dirichlet elliptic problems with discontinuous nonlinearity
Ziqing Yuan and Jianshe YuNonlinear Analysis 197 111848 (2020)
https://doi.org/10.1016/j.na.2020.111848
Multiplicity and concentration results for a fractional Schrödinger-Poisson type equation with magnetic field
Vincenzo AmbrosioProceedings of the Royal Society of Edinburgh: Section A Mathematics 150 (2) 655 (2020)
https://doi.org/10.1017/prm.2018.153
Fractional Schrodinger-Poisson systems with weighted Hardy potential and critical exponent
Yu Su, Haibo Chen, Senli Liu and Xianwen FangElectronic Journal of Differential Equations 2020 (01-132) 01 (2020)
https://doi.org/10.58997/ejde.2020.01
Positive and sign-changing least energy solutions for a fractional Schrödinger–Poisson system with critical exponent
Yuanyang Yu, Fukun Zhao and Leiga ZhaoApplicable Analysis 99 (13) 2229 (2020)
https://doi.org/10.1080/00036811.2018.1557325
Least energy sign-changing solutions for the fractional Schrödinger–Poisson systems in R 3 $\mathbb{R}^{3}$
Da-Bin Wang, Yu-Mei Ma and Wen GuanBoundary Value Problems 2019 (1) (2019)
https://doi.org/10.1186/s13661-019-1128-x
Ground state sign-changing solutions for a class of nonlinear fractional Schrödinger–Poisson system with potential vanishing at infinity
Da-Bin Wang, Hua-Bo Zhang, Yu-Mei Ma and Wen GuanJournal of Applied Mathematics and Computing 61 (1-2) 611 (2019)
https://doi.org/10.1007/s12190-019-01265-y
The concentration behavior of ground state solutions for a critical fractional Schrödinger–Poisson system
Zhipeng Yang, Yuanyang Yu and Fukun ZhaoMathematische Nachrichten 292 (8) 1837 (2019)
https://doi.org/10.1002/mana.201700398
Existence and nonexistence of positive solutions for a static Schrödinger–Poisson–Slater equation
Zhisu Liu, Zhitao Zhang and Shuibo HuangJournal of Differential Equations 266 (9) 5912 (2019)
https://doi.org/10.1016/j.jde.2018.10.048
Concentration behavior of ground state solutions for a fractional Schrödinger–Poisson system involving critical exponent
Zhipeng Yang, Yuanyang Yu and Fukun ZhaoCommunications in Contemporary Mathematics 21 (06) 1850027 (2019)
https://doi.org/10.1142/S021919971850027X
INFINITELY MANY SOLUTIONS FOR A ZERO MASS SCHRÖDINGER-POISSON-SLATER PROBLEM WITH CRITICAL GROWTH
Liu Yang and Zhisu LiuJournal of Applied Analysis & Computation 9 (5) 1706 (2019)
https://doi.org/10.11948/20180273
Multiplicity of Positive Solutions for Schrödinger–Poisson Systems with a Critical Nonlinearity in $$\mathbb {R}^3$$ R 3
Weihong Xie, Haibo Chen and Hongxia ShiBulletin of the Malaysian Mathematical Sciences Society 42 (5) 2657 (2019)
https://doi.org/10.1007/s40840-018-0623-z
Ground state solutions for the non-linear fractional Schrödinger–Poisson system
Kaimin TengApplicable Analysis 98 (11) 1959 (2019)
https://doi.org/10.1080/00036811.2018.1441998
Existence and multiplicity of normalized solutions for the nonlinear Kirchhoff type problems
Weihong Xie and Haibo ChenComputers & Mathematics with Applications 76 (3) 579 (2018)
https://doi.org/10.1016/j.camwa.2018.04.038
Existence of nontrivial solutions for fractional Schrödinger‐Poisson system with sign‐changing potentials
Guofeng Che, Haibo Chen, Hongxia Shi and Zewei WangMathematical Methods in the Applied Sciences 41 (13) 5050 (2018)
https://doi.org/10.1002/mma.4951
Existence and concentration of positive ground state solutions for nonlinear fractional Schrödinger‐Poisson system with critical growth
Kaimin Teng and Ravi P. AgarwalMathematical Methods in the Applied Sciences 41 (17) 8258 (2018)
https://doi.org/10.1002/mma.5289
The existence of nontrivial solution for a class of sublinear biharmonic equations with steep potential well
Yu Su and Haibo ChenBoundary Value Problems 2018 (1) (2018)
https://doi.org/10.1186/s13661-018-0949-3
Existence of positive ground state solutions for fractional Schrödinger equations with a general nonlinearity
Zhisu Liu and Zigen OuyangApplicable Analysis 97 (7) 1154 (2018)
https://doi.org/10.1080/00036811.2017.1307963
The existence of nontrivial solution for biharmonic equation with sign‐changing potential
Yu Su and Haibo ChenMathematical Methods in the Applied Sciences 41 (16) 6170 (2018)
https://doi.org/10.1002/mma.5127
Multiple solutions for the Schrödinger equations with sign-changing potential and Hartree nonlinearity
Guofeng Che and Haibo ChenApplied Mathematics Letters 81 21 (2018)
https://doi.org/10.1016/j.aml.2017.12.014
Infinitely many solutions for a class of superlinear Dirac–Poisson system
Wen Zhang, Jian Zhang and Weijin JiangApplied Mathematics Letters 80 79 (2018)
https://doi.org/10.1016/j.aml.2018.01.009
Ground state of solutions for a class of fractional Schrödinger equations with critical Sobolev exponent and steep potential well
Liuyang Shao and Haibo ChenMathematical Methods in the Applied Sciences 40 (18) 7255 (2017)
https://doi.org/10.1002/mma.4527