Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (2): 442-453.
Previous Articles Next Articles
Mengxue Du,Fanghui Li,Zhengping Wang*()
Received:
2021-06-23
Online:
2022-04-26
Published:
2022-04-18
Contact:
Zhengping Wang
E-mail:zpwang@whut.edu.cn
Supported by:
CLC Number:
Mengxue Du, Fanghui Li, Zhengping Wang. Multiplicity of Normalized Solutions for Nonlinear Schrödinger-Poisson Equation with Hardy Potential[J].Acta mathematica scientia,Series A, 2022, 42(2): 442-453.
Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks
1 |
D'Aprile T , Mugnai D . Solitary waves for the nonlinear Klein-Gordon-Maxwell and Schrödinger-Maxwell equations. Proceedings of the Royal Society of Edinburgh, 2004, 134 (5): 893- 906
doi: 10.1017/S030821050000353X |
2 |
Ruiz D . The Schrödinger-Poisson equation under the effect of a nonlinear local term. Journal of Functional Analysis, 2006, 237 (2): 655- 674
doi: 10.1016/j.jfa.2006.04.005 |
3 |
Ambrosetti A . On Schrödinger-Poisson systems. Milan Journal of Mathematics, 2008, 76 (1): 257- 274
doi: 10.1007/s00032-008-0094-z |
4 |
Bellazzini J , Jeanjean L , Luo T J . Existence and instability of standing waves with prescribed norm for a class of Schrödinger-Poisson equations. Proceedings of the London Mathematical Society, 2013, 107 (2): 303- 339
doi: 10.1112/plms/pds072 |
5 |
Li G B , Peng S J , Yan S S . Infinitely many positive solutions for the nonlinear Schrödinger-Poisson system. Communications in Contemporary Mathematics, 2010, 12 (6): 1069- 1092
doi: 10.1142/S0219199710004068 |
6 |
Jiang Y S , Zhou H S . Multiple solutions for a Schrödinger-Poisson-Slater equation with external Coulomb potential. Science China Mathematics, 2014, 57 (6): 1163- 1174
doi: 10.1007/s11425-014-4790-6 |
7 |
Luo T J . Multiplicity of normalized solutions for a class of nonlinear Schrödinger-Poisson-Slater equations. Journal of Mathematical Analysis and Applications, 2014, 416 (1): 195- 204
doi: 10.1016/j.jmaa.2014.02.038 |
8 | Wang Z P , Zhou H S . Sign-changing solutions for the nonlinear Schrödinger-Poisson system in $R^3$. Calculus of Variations and Partial Differential Equations, 2015, 52 (3): 927- 943 |
9 |
Zeng X Y , Zhang L . Normalized solutions for Schrödinger-Poisson-Slater equations with unbounded potentials. Journal of Mathematical Analysis and Applications, 2017, 452 (1): 47- 61
doi: 10.1016/j.jmaa.2017.02.053 |
10 |
Bartsch T , De Valeriola S . Normalized solutions of nonlinear Schrödinger equations. Archiv der Mathematik, 2013, 100 (1): 75- 83
doi: 10.1007/s00013-012-0468-x |
11 |
Jeanjean L . Existence of solutions with prescribed norm for semilinear elliptic equations. Nonlinear Analysis, 1997, 28 (10): 1633- 1659
doi: 10.1016/S0362-546X(96)00021-1 |
12 |
Berestycki H , Lions P L . Nonlinear scalar field equations, Ⅱ Existence of infinitely many solutions. Archive for Rational Mechanics and Analysis, 1983, 82 (4): 347- 375
doi: 10.1007/BF00250556 |
[1] | Meng Xiaoying,Lu Lu. Existence and Asymptotic Behavior of Solutions for Kirchhoff Equations Involving the Fractional $ p$-Laplacian [J]. Acta mathematica scientia,Series A, 2025, 45(2): 434-449. |
[2] | Zhang Qian. Normalized Solutions of the Quasilinear Schrödinger System in Bounded Domains [J]. Acta mathematica scientia,Series A, 2025, 45(1): 1-30. |
[3] | Sun Xin, Duan Yu. Multiplicity of Solutions for Sublinear Klein-Gordon-Maxwell Systems [J]. Acta mathematica scientia,Series A, 2024, 44(5): 1205-1215. |
[4] | Jin Zhenfeng, Sun Hongrui, Zhang Weimin. Multiplicity and Asymptotic Behavior of Normalized Solutions for Kirchhoff-Type Equation [J]. Acta mathematica scientia,Series A, 2024, 44(4): 871-884. |
[5] | Wen Ruijiang, Liu Fanqin, Xu Ziyi. Multiplicity of Positive Solutions to Subcritical Choquard Equation [J]. Acta mathematica scientia,Series A, 2024, 44(1): 60-79. |
[6] | Li Renhua, Wang Zhengping. Normalized Solution of Fractional Schrödinger-Poisson Equations with Coercive Potential [J]. Acta mathematica scientia,Series A, 2023, 43(6): 1723-1730. |
[7] | Fan Shishi, Li Haixia, Lu Yindou. Dynamics Analysis of a Diffusive Predator-Prey Model with Beddington-DeAngelis Function Response and Harvesting [J]. Acta mathematica scientia,Series A, 2023, 43(6): 1929-1942. |
[8] | Li Xiaodong, Gao Hongliang, Xu Jing. Exact Multiplicity of Positive Solutions for a Semipositone Mean Curvature Problem with Concave Nonlinearity [J]. Acta mathematica scientia,Series A, 2023, 43(5): 1341-1349. |
[9] | Gui Kunming,Tao Hongshan,Yang Jun. Normalized Ground States for the Quasi-linear Schrödinger Equation with Combined Nonlinearities [J]. Acta mathematica scientia,Series A, 2023, 43(4): 1062-1072. |
[10] | Nan Deng,Meiqiang Feng. Positive Doubly Periodic Solutions To Telegraph Equations: Existence, Uniqueness, Multiplicity and Asymptotic Behavior [J]. Acta mathematica scientia,Series A, 2022, 42(5): 1360-1380. |
[11] | Tong Zhao,Hailong Yuan,Gaihui Guo. Positive Solutions of a Predator-Prey Model with Modified Leslie-Gower Type [J]. Acta mathematica scientia,Series A, 2022, 42(1): 176-186. |
[12] | Yuan Haihua, Zhang Zhengjie, Xu Guojin. Multiple Solutions for Semilinear Elliptic Equations with Critical Exponents and Hardy Potential [J]. Acta mathematica scientia,Series A, 2016, 36(6): 1137-1144. |
[13] | Li Qin, Yang Zuodong. Multiple Solutions for a Class of Quasilinear Nonhomogeneous Elliptic Systems with Nonlinear Boundary Conditions [J]. Acta mathematica scientia,Series A, 2016, 36(2): 307-316. |
[14] | Sun Zhaohong, Zhang Wei, He Tieshan, Gao Chuanxiang. Multiplicity Result for Homoclinic Solutions to A Class of Subquadratic Hamiltonian Systems [J]. Acta mathematica scientia,Series A, 2015, 35(2): 364-372. |
[15] | WANG Hua, Alatanchang, HUANG Jun-Jie. Multiplicity and Completeness of a Class of |Hamiltonian |Operators and Its Applications [J]. Acta mathematica scientia,Series A, 2014, 34(6): 1507-1517. |
|