全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

Ground State Solutions for p-Fractional Choquard-Kirchhoff Equations Involving Electromagnetic Fields and Critical Nonlinearity

DOI: 10.4236/oalib.1108837, PP. 1-16

Subject Areas: Functional Analysis

Keywords: Fractional Choquard-Kirchhoff Equation, Magnetic Fractional p-Laplacian, Critical Growth

Full-Text   Cite this paper   Add to My Lib

Abstract

This paper is concerned with the existence of ground state solutions for p-fractional Choquard-Kirchhoff equations involving electromagnetic fields and critical nonlinearity. Under assumptions on the nonlinear term, by applying the method of Nehari manifold, we obtain that the equation possesses a ground state solution.

Cite this paper

Yan, X. (2022). Ground State Solutions for p-Fractional Choquard-Kirchhoff Equations Involving Electromagnetic Fields and Critical Nonlinearity. Open Access Library Journal, 9, e8837. doi: http://dx.doi.org/10.4236/oalib.1108837.

References

[1]  D’Avenia, P. and Squassina, M. (2018) Ground States for Fractional Magnetic Operators. ESAIM, 24, 1-24. https://doi.org/10.1051/cocv/2016071
[2]  Ichinose, T. (1993) On Essential Selfadjointness of the Weyl Quantized Relativistic Hamiltonian. Forum Mathematicum, 5, 539-560. https://doi.org/10.1515/form.1993.5.539
[3]  Ichinose, T. and Tamura, H. (1986) Imaginary-Time Path Integral for a Relativistic Spinless Particle in an Electromagnetic Field. Communications in Mathematical Physics, 105, 239-257. https://doi.org/10.1007/BF01211101
[4]  Ambrosio, V. and D ‘Avenia, P. (2018) Nonlinear Fractional Magnetic Schrödinger Equation: Existence and Multiplicity. Journal of Differential Equations, 264, 3336-3368. https://doi.org/10.1016/j.jde.2017.11.021
[5]  Liang, S., Repovs, D. and Zhang, B. (2018) On the Fractional Schrödinger-Kirchhoff Equations with Electromagnetic Fields and Critical Nonlinearity. Computers and Mathematics with Applications, 75, 1778-1794. https://doi.org/10.1016/j.camwa.2017.11.033
[6]  Xiang, M., Zhang, B. and Guo, X. (2015) Infinitely Many Solutions for a Fractional Kirchhoff Type Problem via Fountain Theorem. Nonlinear Analysis, 120, 299-313. https://doi.org/10.1016/j.na.2015.03.015
[7]  Guo, Y. and Nie. J. (2015) Existence and Multiplicity of Nontrivial Solutions for P-Laplacian Schrödinger-Kirchhoff-Type Equations. Journal of Mathematical Analysis and Applications, 428, 1054-1069. https://doi.org/10.1016/j.jmaa.2015.03.064
[8]  Li, Q., Wang, W., Teng, K. and Wu, X. (2020) Ground States for Fractional Schrödinger Equations with Electromagnetic Fields and Critical Growth. Acta Mathematica Scientia, 40, 59-74. https://doi.org/10.1007/s10473-020-0105-0
[9]  Wang, L., Han, T. and Wang, J.X. (2021) Infinitely Many Solutions for Schrödinger-Choquard-Kirchhoff Equations Involving the Fractional p-Laplacian. Acta Mathematica Sinica, English Series, 37, 315-332. https://doi.org/10.1007/s10114-021-0125-z
[10]  Ambrosio, V. (2019) Multiplicity and Concentration of Solutions for a Fractional Kirchhoff Equation with Magnetic Field and Critical Growth. Annales Henri Poincaré, 20, 2717-2766. https://doi.org/10.1007/s00023-019-00803-5
[11]  Xiang, M., Radulescu, V.D. and Zhang. B. (2018) A Critical Fractional Choquard-Kirchhoff Problem with Magnetic Field. Communications in Contemporary Mathematics, 21, Article ID: 1850004. https://doi.org/10.1142/S0219199718500049
[12]  Ferrara. M., Zhang. B. and Xiang, M. (2015) Existence of Solutions for Kirchhoff Type Problem Involving the Non-Local Fractional P-Laplacian. Journal of Mathematical Analysis and Applications, 424, 1021-1041. https://doi.org/10.1016/j.jmaa.2014.11.055
[13]  Iannizzotto, A., Liu, S., Perera, K. and Squassina, M. (2014) Existence Results for Fractional P-Laplacian Problems via Morse Theory. Advances in Calculus of Variations, 9, 101-125. https://doi.org/10.1515/acv-2014-0024
[14]  Radulescu, V.D., Xiang, M. and Zhang, B. (2016). Existence of Solutions for Perturbed Fractional p-Laplacian Equations. Journal of Differential Equations, 260, 1392-1413. https://doi.org/10.1016/j.jde.2015.09.028
[15]  Shen, Z., Gao, F. and Yang, M. (2016) Ground States for Nonlinear Fractional Choquard Equations with General Nonlinearities. Mathematical Methods in the Appliedences, 39, 4082-4098. https://doi.org/10.1002/mma.3849
[16]  Ma, P. and Zhang, J. (2017) Existence and Multiplicity of Solutions for Fractional Choquard Equations. Nonlinear Analysis, 164, 100-117. https://doi.org/10.1016/j.na.2017.07.011
[17]  Li, Q., Teng, K. and Zhang, J. (2020) Ground State Solutions for Fractional Choquard Equations Involving upper Critical Exponent. Nonlinear Analysis, 197, Article ID: 111846. https://doi.org/10.1016/j.na.2020.111846
[18]  Wang, F. and Xiang, M. (2017) Multiplicity of Solutions for a Class of Fractional Choquard-Kirchhoff Equations Involving Critical Nonlinearity. Analysis and Mathematical Physics, 9, 1-16. https://doi.org/10.1007/s13324-017-0174-8
[19]  Guo, Y.H., Sun, H.R. and Cui, N. (2021) Existence and Multiplicity Results for the Fractional Magnetic Schrödinger Equations with Critical Growth. Journal of Mathematical Physics, 62, Article ID: 061503. https://doi.org/10.1063/5.0041372
[20]  Xiang, M., Pucci, P., Squassina, M. and Zhang, B. (2017) Nonlocal Schrödinger-Kirchhoff Equations with External Magnetic Field. Discrete and Continuous Dynamical Systems, 37, 1631-1649. https://doi.org/10.3934/dcds.2017067
[21]  Pucci, P., Xiang, M. and Zhang, B. (2017) Existence Results for Schrödinger-Choquard-Kirchhoff Equations Involving the Fractional P-Laplacian. Advances in Calculus of Variations, 12, 253-275. https://doi.org/10.1515/acv-2016-0049
[22]  Huang, L., Wang, L. and Feng, S. (2021) Ground State Solutions for Fractional Schrödinger-Choquard-Kirchhoff Type Equations with Critical Growth. Complex Variables and Elliptic Equations, 67, 1624-1638. https://doi.org/10.1080/17476933.2021.1890051
[23]  Li, Q., Teng, K. and Wu, X. (2018) Ground States for Fractional Schrödinger Equations with Critical Growth. Journal of Mathematical Physics, 59, Article ID: 033504. https://doi.org/10.1063/1.5008662
[24]  Di Nezza, E., Palatucci, G. and Valdinoci, E. (2012) Hitchhiker’s Guide to the Fractional Sobolev Spaces. Bulletin des Sciences Mathématiques, 136, 521-573. https://doi.org/10.1016/j.bulsci.2011.12.004
[25]  Lieb, E.H. and Loss, M. (2001) Analysis, Second Edition. American Mathematical Society, Providence. https://doi.org/10.1090/gsm/014
[26]  Szulkin, A. and Weth, T. (2010) The Method of Nehari Manifold. In: Gao, D.Y. and Motreanu, D., Eds., Handbook of Nonconvex Analysis and Applications, International Press, Somerville, 597-632.
[27]  Willem, M. (1996) Minimax Theorems. Progress in Nonlinear Differential Equations and their Applications Vol. 24, Birkhäuser, Boston. https://doi.org/10.1007/978-1-4612-4146-1
[28]  Zhang, H., Xu, J. and Zhang, F. (2015) Existence and Multiplicity of Solutions for Superlinear Fractional Schrdinger Equations in . Journal of Mathematical Physics, 56, Article ID: 091502. https://doi.org/10.1063/1.4929660
[29]  Tao, F. and Wu, X. (2017) Existence and Multiplicity of Positive Solutions for Fractional Schrödinger Equations with Critical Growth. Nonlinear Analysis: Real World Applications, 35, 158-174. https://doi.org/10.1016/j.nonrwa.2016.10.007

Full-Text


comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133

WeChat 1538708413