Schrödinger-Bopp-Podolsky-Proca 系统——献给陈化教授 70 寿辰

Acta mathematica scientia,Series A ›› 2026, Vol. 46 ›› Issue (2): 751-769.

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On the Schrödinger-Bopp-Podolsky-Proca System with Singular Nonlinearity on Closed Manifolds

Jiaqing Bao¹(), Nanbo Chen¹^,^*(), Xiaochun Liu²(), Sainan Liang²()

¹ School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guangxi Guilin 541004
² School of Mathematics and Statistics, Wuhan University, Wuhan 430072

Received:2026-01-14 Revised:2026-02-02 Online:2026-04-26 Published:2026-04-27
Contact: Nanbo Chen E-mail:18155929548@163.com;flyingnb@126.com;xcliu@whu.edu.cn;snliang365@163.com
Supported by:
Guangxi Natural Science Foundation(2023GXNSFBA026197);National College Student Innovation Training Program(202410595034);NSFC(12131017);NSFC(12071364)

Abstract

CLC Number:

O175.29

Jiaqing Bao, Nanbo Chen, Xiaochun Liu, Sainan Liang. On the Schrödinger-Bopp-Podolsky-Proca System with Singular Nonlinearity on Closed Manifolds[J].Acta mathematica scientia,Series A, 2026, 46(2): 751-769.

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References 19

[1]	Alves R L. Generalized Schrödinger-Bopp-Podolsky type system with singular nonlinearity. J Math Anal Appl, 2024, 539(1): Art 128499
[2]	Ambrosetti A, Rabinowitz P H. Dual variational methods in critical point theory and applications. J Functional Analysis, 1973, 14: 349-381
[3]	Brézis H, Kato T. Remarks on the Schrödinger operator with singular complex potentials. J Math Pures Appl, 1979, 58(2): 137-151
[4]	Chen S, Tang X. On the critical Schrödinger-Bopp-Podolsky system with general nonlinearities. Nonlinear Anal, 2020, 195: Art 111734
[5]	d'Avenia P, Ghimenti M G. Multiple solutions and profile description for a nonlinear Schrödinger-Bopp-Podolsky-Proca system on a manifold. Calc Var Partial Differential Equations, 2022, 61(6): Art 223
[6]	d'Avenia P, Siciliano G. Nonlinear Schrödinger equation in the Bopp-Podolsky electrodynamics: solutions in the electrostatic case. J Differential Equations, 2019, 267(2): 1025-1065
[7]	Ekeland I. On the variational principle. J Math Anal Appl, 1974, 47: 324-353
[8]	Gao Y. Nonlinear Schrödinger equation in the Bopp-Podolsky electrodynamics: global boundedness, blowup and no scattering in the energy space. J Differential Equations, 2023, 357: 64-97
[9]	Hebey E. Introduction à l'analyse Non Linéaire Sur Les Variétés. Paris: Diderot Editeur, 1997
[10]	Hebey E. Electro-magneto-static study of the nonlinear Schrödinger equation coupled with Bopp-Podolsky electrodynamics in the Proca setting. Discrete Contin Dyn Syst, 2019, 39(11): 6683-6712
[11]	Hebey E. Strong convergence of the Bopp-Podolsky-Schrödinger-Proca system to the Schrödinger-Poisson-Proca system in the electro-magneto-static case. Calc Var Partial Differential Equations, 2020, 59(6): Art 198
[12]	Hebey E. Blowing-up solutions to Bopp-Podolsky-Schrödinger-Proca and Schrödinger-Poisson-Proca systems in the electro-magneto-static case. Adv Differential Equations, 2022, 27(5/6): 253-332
[13]	Huang J, Wang S. Normalized ground states for the mass supercritical Schrödinger-Bopp-Podolsky system: existence, uniqueness, limit behavior, strong instability. J Differential Equations, 2025, 437: Art 113282
[14]	Liang S, Chen N, Liu X. Positive solutions for Schrödinger-Poisson system with singularity on compact Riemannian manifolds. Commun Pure Appl Anal, 2025, 24(9): 1627-1649
[15]	Struwe M. Variational Methods. Berlin: Springer-Verlag, 2008
[16]	Talluri M. A multiplicity result for a double perturbed Schrödinger-Bopp-Podolsky-Proca system. J Math Anal Appl, 2024, 540(2): Art 128648
[17]	Teng K, Yan Y. Existence of a positive bound state solution for the nonlinear Schrödinger-Bopp-Podolsky system. Electron J Qual Theory Differ Equ, 2021, 4: 1-19
[18]	Zhang Z. Sign-changing solutions for a class of Schrödinger-Bopp-Podolsky system with concave-convex nonlinearities. J Math Anal Appl, 2024, 530(1): Art 127712
[19]	Zhu Y, Chen C, Chen J. The Schrödinger-Bopp-Podolsky equation under the effect of nonlinearities. Bull Malays Math Sci Soc, 2021, 44(2): 953-980

On the Schrödinger-Bopp-Podolsky-Proca System with Singular Nonlinearity on Closed Manifolds

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