郑神州

基本信息

教育背景

• 1994/09-1997/07  复旦大学数学研究所, 博士研究生；
• 1991/09-1994/07  北京师范大学数学系, 硕士研究生

研究和工作经历:

•  2017/11-2018/02  西班牙巴斯克应用数学中心合作研究项目,访问Luis Vega教授；
•  2017/05-2017/07  西班牙巴斯克应用数学中心合作研究项目,访问Luis Vega教授(西班牙皇家科学院院士，欧洲科学院院士)；   
•  2013/07-2013/08  南开大学陈省身数学研究所, 访问教授;
•  2011/09-2012/09  美国肯塔基大学,芝加哥大学,德克萨斯大学访问学者;
•  2008/02-2008/05  美国University of Texas-Pan American,访问教授;
•  2007/09-2007/10  南开大学陈省身数学研究所,访问教授;
•  2005/10-现在    北京交通大学理学院 教授
•  2002/08-2002/12  中国科学院 系统科学研究所,访问学者;
•  2001/02-2001/06  中国科学院应用数学研究所,访问学者;
•  2000/01-2005/10  北京交通大学理学院 副教授；
•  1997/07-2000/01  北京交通大学理学院 讲师 

工作经历

• 研究兴趣:  微分方程理论及应用；特殊函数；不确定性原理；统计力学模型在金融数学应用。
• 近期成果:（1）首次将格林函数应用于非线性偏微分方程的正则性研究, 克服了因非线性问题而造成格林函数和基本解应用的困境。 (2)证实Baricz关于修正Bessel函数商函数的严格对数凸性的猜想；解决了Hornik-Grun涉及特殊函数在参数(-1,-1/2)的公开问题。(3) 依据分层材料和电流变力学等物理背景，在弱条件下建立了一系列标准和非标准增长的椭圆和抛物方程问题广义Calderon-Zygmund型理论，使得该理论在多方面得到推进和拓展。（4）建立到Riemann流形上双调和映射能量的量子化，得到奇异点能量的有限泡泡过程; 当目标流形为球面时达到更优结果。在Transactions of Amer. Math. Soc., J. Functional Analysis, J. Differential Equations,Calc. Var. and PDE, Manuscripta Math., Proceedings of Amer. Math. Soc., Discrete Conti. Dyn. Syst. A/B, Nonlinear Analysis A/B, J. Math. Anal. Appl., Mathematische Nachrichten, Complex Variables and Elliptic Equations, Results in Mathematics, Dynamics of  Part. Diff. Equ., Elect. Journal Differential Equations, IMA J. Applied Math., Z. angew. Math. Phys., Diff. and Integral Equ., Comm. Pure  Appl. Anal., Mediteranean J. Math.等发表了100余篇SCI论文。

       数学是科学研究的共同语言。世界是多元、变化的，万物都是随时-空变化而演化；如何科学、定量地刻划万物的演化呢？偏微分方程是研究时-空变化物理规律的数学；科学研究有两大基本任务:一是从已知值推断未知量，即所谓:从外围已知数据推算内在规律(如稳态下的各种边值问题)；二是从现在状态预测未来演化规律(始值问题、初边值混合问题)，这正是我们所要研究的本质所在。欢迎大家一起参与！

研究方向

• 微分方程理论与应用
• 金融统计分析
• 应用数学

招生专业

• 应用数学硕士
• 统计学硕士
• 应用数学博士
• 数学博士
• 数学硕士

科研项目

• 国家自然科学基金“面上”项目：弱正则数据下非标准增长的椭圆和抛物方程的正则性研究，2021-01-01--2024-12-31
• 国家自然科学基金"国际合作"项目: 调和分析与微分方程, 2016-09-010--2018-01-31
• 国家自然科学基金“面上”项目：抛物和椭圆型方程和方程组的若干问题，2014-01-01--2017-12-31
• 国家自然科学基金“面上”项目：具间断系数非线性退化椭圆问题的正则性研究，2011-01-01--2013-12-31
• 国家自然科学基金“面上”项目：与平均曲率有关的非线性椭圆方程，2007-01-01--2009-12-31

教学工作

本科课程：高等数学、线性代数、几何代数、复变函数与积分变换、数学物理方程、偏微分方程、概率论和数理统计、计算方法、运筹学等。

研究生课程：偏微分方程概论、应用偏微分方程、Sobolev空间、椭圆偏微分方程、抛物性偏微分方程、数值分析、特殊函数等。

论文/期刊

2024

1. Gradient estimates for a class of higherorder elliptic equations of p-growth over a nonsmooth domain,Advances in Nonlinear Analysis 2024; 13: 20230132(with Tian H.)
2. Besov regularity for a class of elliptic obstacle problems with double-phase Orlicz growth,J. Math. Anal. Appl. 535 (2024) 128119 (with Zhao L.).

2023 

1. Gradient estimates of general nonlinear singular elliptic equations with measure data.J. Differential Equations 372 (2023), 402–457(with Lin X. and Feng Z.)
2. Multiplicity and concentration of solutions for a class of magnetic Schrödinger-Poisson system with double critical growths. Z. Angew. Math. Phys. 74 (2023), no. 3, Paper No. 94, 33 pp(with Lin X.)
3. Multiple solutions of p-fractional Schrödinger-Choquard-Kirchhoff equations with Hardy-Littlewood-Sobolev critical exponents, Adv. Nonlinear Stud. 23 (2023), no. 1, Paper No. 20220059, 21 pp (with Lin X. and Feng Z.).
4.  On a class of fractional Kirchhoff-Schrödinger-Poisson systems involving magnetic fields.Commun. Nonlinear Sci. Numer. Simul. 124 (2023), Paper No. 107312, 24 pp(with Lin X.)
5. Global gradient estimates for general nonlinear elliptic measure data problems with Orlicz growth.J. Math. Anal. Appl. 524 (2023), no. 1, Paper No. 127080, 36 pp (with Zhang J.)
6. Tighter Heisenberg-Weyl type uncertainty principle associated with quaternion wavelet transform.J. Pseudo-Differ. Oper. Appl. 14 (2023), no. 1, Paper No. 14, 27 pp (with Wang X.)
7. Gradient estimate for asymptotically regular elliptic equations of double phase with variable exponents. Math. Nachr. 296 (2023), no. 2, 701–715. (with Liang S.)
8.  W1,γ(⋅)-estimate to non-uniformly elliptic obstacle problems with borderline growth.Complex Var. Elliptic Equ. 68 (2023), no. 10, 1833–1856 (with Zhang X.)
9. Boundedness on generalized Morrey spaces for the Schrödinger operator with potential in a reverse Hölder class. Electron. J. Differential Equations(2023), Paper No. 67, 14 pp (with Wang G.).

2022

1.  Existence and multiplicity for fractional p-Kirchhoff problem with competitive nonlinearities and critical growth. Anal. Math. Phys. 12 (2022), no. 4, Paper No. 96, 30 pp (with Lv H.).
2. Ground states for Schrödinger-Kirchhoff equations of fractional p-Laplacian involving logarithmic and critical nonlinearity. Commun. Nonlinear Sci. Numer. Simul. 111 (2022), Paper No. 106438, 15 pp. (with Lv H.)
3. Mixed local and nonlocal Schrödinger-Poisson type system involving variable exponents.Electron. J. Differential Equations(2022), Paper No. 81, 16 pp(with Lin X.)
4.  Calderón-Zygmund estimate for asymptotically regular elliptic equations with Lp(x)-logarithmic growth.Complex Var. Elliptic Equ. 67 (2022), no. 1, 61–78. (with Liang S.)
5. Gradient estimates in anisotropic Lorentz spaces to general elliptic equations of p-growth. Rocky Mountain J. Math. 52 (2022), no. 2, 727–748 (with Tian H.)
6.  Weighted Lorentz estimates for fully nonlinear elliptic equations with oblique boundary data, Journal of Elliptic and Parabolic Equations,  (2022) 8:255–281. (with Zhang J.)
7.  On new sharp bounds for the Toader-Qi mean involved in the modified Bessel functions of the first kind.J. Math. Inequal. 16 (2022), no. 2, 609–628(with Li C. and Liu Z.M.)
8.  W1,p(·)-regularity for a class of non-uniformly elliptic problems with Orlicz growth. Mediterranean Journal of Mathematics19 (2022), no. 6, Paper No. 255, 30 pp, (with S. Liang and H. Gao)
9.  An optimal gradient estimate for asymptotically regular variational integrals with multi-phase. Rocky Mountain J Math.52 (2022), no. 6, 2071–2084 (with Liang S.)

2021

1. Liang, Shuang; Zheng, Shenzhou, Gradient estimate of a variable power for nonlinear elliptic equations with Orlicz growth. Adv. Nonlinear Analysis, 10 (2021), no. 1, 172–193
2. Xiaolin Zhang; Shenzhou Zheng, Besov regularity for the gradients of solutions to non-uniformly elliptic obstacle problems, Journal of Mathematical Analysis and Applications,  504 (2021),123924
3. Liang, Shuang; Zheng, Shenzhou, Lorentz estimates to nonlinear elliptic obstacle problems of p(x)-growth in Reifenberg domains, Journal of Mathematical Analysis and Applications, 501 (2021),125402
4. Hong Tian,  Zheng, Shenzhou, The W1,2(p,q)‑solvability for a class of fully nonlinear parabolic equations, Journal of Elliptic and Parabolic Equations, 7: 25–45 (2021)
5. Liang, Shuang; Zheng, Shenzhou, The Calderón–Zygmund estimates for a class of nonlinear elliptic equations with measure data. Mathematische Nachrichten, 2021,1–13,DOI:10.1002/mana.201800334
6. Lv, Huilin; Zheng, Shenzhou; Feng, Zhaosheng Existence results for nonlinear Schrödinger equations involving the fractional (p,q)-Laplacian and critical nonlinearities. Electron. J. Differential Equations, 2021, Paper No. 100, 24 pp.
7. Xiaoyu Zhu, Shenzhou Zheng,On uncertainty principle for the two-sided quaternion linear canonical transform, Journal of Pseudo-Differential Operators and Applications, (2021) 12:3,  doi.org/10.1007/s11868-021-00395-x
8. Guochao Wang, Shenzhou Zheng, Jun Wang, Nonlinear fluctuation behaviors of complex voter financial price dynamics on small-world network, Nonlinear Dynamics, 103: 2525–2545 (2021)
9. Xiaoyu Zhu, Shenzhou Zheng,Uncertainty principles for the two-sided offset quaternion linear canonical transform, Mathematical Methods in the Applied Sciences, 2021;44:14236-14255 
10. Junjie Zhang,Shenzhou Zheng,Chunyan Zuo, $W^{2,p}$-regularity for asymptotically regular fully nonlinear elliptic and parabolic equations with oblique boundary values, Discrete & Continuous Dynamical Systems - Series S, 2021,doi:10.3934/dcdss.2021080
11. Xiaolu Lin, Shenzhou Zheng; Multiplicity and asymptotic behavior of solutions to fractional (p,q)-Kirchhoff type problems with critical Sobolev-Hardy exponent, Electron. J. Differential Equations,2021 (2021), No. 66, pp. 1-20.

2020

1. Zhang, Junjie; Zheng, Shenzhou; Yu, Haiyan Lp(⋅)-regularity of Hessian for nondivergence parabolic and elliptic equations with measurable coefficients.Commun. Pure Appl. Anal. 19 (2020), no. 5, 2777–2796
2. Junjie Zhang;Shenzhou Zheng;Zhaosheng Feng;Weighted Lp(·)-regularity for fully nonlinear parabolic equations. Calc. Var. and PDE, (2020) 59:190
3. Zhang, Junjie; Zheng, Shenzhou Weighted gradient estimates for general nonlinear elliptic equations involving measure data.Journal of Mathematical Analysis and Applications 488 (2020), no.1, 124048, 51 pp
4. Liang, Shuang; Zheng, Shenzhou Variable Lorentz estimate for conormal derivative problems of stationary Stokes system with partially BMO coefficients. Nonlinear Analysis 194 (2020), 111355, 24 pp. 
5. Tian, Hong; Zheng, Shenzhou Orlicz estimates for general parabolic obstacle problems withp(t,x)-growth in Reifenberg domains. Electron. J. Differential Equations 2020, Paper No. 3, 25 pp.
6. Zhang, Junjie; Zheng, Shenzhou Sobolev regularity for quasilinear parabolic equations with asymptotically regular nonlinearity. Appl. Math. Lett. 103 (2020), 106211, 8 pp.
7. Zhang, Junjie; Zheng, Shenzhou Hessian estimates for nondivergence parabolic and elliptic equations with partially BMO coefficients. Results Math. 75 (2020), no. 1, Paper No. 21, 31 pp.
8. Liang, Shuang; Zheng, Shenzhou Calderón-Zygmund estimate for asymptotically regular non-uniformly elliptic equations. Journal of Mathematical Analysis and Applications 484 (2020), no. 2,123749, 17pp. 
9. Xiaoyu Zhu, Shenzhou Zheng. Uncertainty Principles for the Two-Sided Quaternion LinearCanonical Transform. Circuits, Systems, and Signal Processing (2020) 39:4436–4458.
10. Wang Guochao, Zheng Shenzhou, Wang Jun, Fluctuation and volatility dynamics of stochastic interacting energy futures price model, Physica A, 517 (2020) 122693.
11. Yang, Zhen-Hang; Xi, Bo-Yan; Zheng, Shen-Zhou Some properties of the generalized Gaussian ratio and their applications. Math. Inequal. Appl. 23 (2020), no. 1, 177–200.

2019   

1. Nonlinear gradient estimates for double phase elliptic problems with irregular double obstacles, Proceedings of AMS,147(9), 2019(with S. Byun and S. Liang)
2. On W1,γ(·)-regularity for nonlinear non-uniformly elliptic equations, manuscripta math. 159, (2019)(with S. Liang)
3. Variable Lorentz estimate for conormal derivative problems of stationary Stokes system with partially BMO coefficients, Nonlinear Analysis, 2019, June，https:// doi.org/ 10.1016/j.na.2018.09.014 (with S. Liang)
4. Weighted Lorentz estimate for asymptotically regular parabolic equations of p(x, t)-Laplaciantype, Nonlinear Analysis, 180 (2019), https://doi.org/ 10.1016/j.na. 2018.10. 013  (with J. Zhang and M. Cai)
5. Morrey regularity for nonlinear elliptic equations with partial BMO nonlinearities under controlled growth, Nonlinear Analysis,180 (2019) (with H. Tian)
6. Lorentz estimate with a variable power for parabolic obstacle problems with non-standard growths, Journal of Differential Equations, 266(2019) (with H. Tian)
7. Variable Lorentz estimate for stationary Stokes system with partially BMO coefficients, Commun. Pure Appl. Anal.18(6), 2019 (with S. Liang)
8. Global integrability of very weak solution to the Dirichlet problem of nonlinear elliptic system,  Electron. J. Differential Equations, Vol. 2019 (2019), No. 1(with Y. Tong and S. Liang)
9. Nonlinear Complexity and Chaotic Behaviors on Finite-Range Stochastic Epidemic Financial Dynamics, International Journal of Bifurcation and Chaos, 29(6) (2019) (with G. Wang and J. Wang)
10. Complex and composite entropy fluctuation behaviors of statistical physics interacting financial model, Physica A, 517 (2019)(with G. Wang and J. Wang)  
11. COMPLETE MONOTONICITY AND INEQUALITES INVOLVING GURLAND’S RATIOS OF GAMMA FUNCTIONS, Mathematical Inequalities & Applications, 22(1) (2019)(with Z. Yang)
12. MONOTONICITY AND INEQUALITIES INVOLVING THE INCOMPLETE GAMMA FUNCTION, Journal of Mathematical Inequalities,13, No 2 (2019)(with H. Lv and Z. Yang)

2018

1. Lorentz estimates for asymptotically regular fully nonlinear parabolic equations, Mathematische Nachrichten, 291(2018) (with J. Zhang)
2. Variable Lorentz estimate for nonlinear elliptic equations with partially regular nonlinearities, Nonlinear Analysis, 172(2018) (with S. Liang)
3. Optimal Morrey estimate for parabolic equations in divergence form via Green's functions, Rocky Mountain Journal of Mathematics, 48(6)(2018) (with J. Zhang)
4. Global regularity in Lorentz spaces for nonlinear elliptic equations with L^{p(\cdot)}\log L-growth, Journal of Mathematical Analysis and Applications,467(2018)(with S. Liang and M. Cai)
5. Weighted Lorentz and Lorentz–Morrey estimates to viscosity solutions of fully nonlinear elliptic equations, Complex Variables and Elliptic Equations, 63(9),2018(with J. Zhang)
6. Orlicz estimates for nondivergence linear elliptic equations with partially BMO coefficients, Complex Variables and Elliptic Equations, 63(6),2018 (with H. Li and J. Zhang)
7. Gradient estimate in Orlicz spaces for elliptic obstacle problems with partially BMO nonlinearities, Electronic Journal of Differential Equations, Vol. 2018 (2018), No. 58(with S. Liang)
8. Another approach of Morrey estimate for linear elliptic equations with partially BMO coefficients in a half space, Filomat, 32:4 (2018) (with H. Tian)
9. Weighted Lorentz estimates for nonlinear elliptic obstacle problems with partially regular nonlinearities, Boundary Value Problems, 2018:115 (with H. Tian)
10. Fuzzy entropy complexity and multifractal behavior of s tatistical physics financial dynamics, Physica A, 506 (2018) (with Y.Wang et al)
11. Modeling and complexity of stochastic interacting Lévy type financial price dynamics, Physica A, 499 (2018)(with Y. Wang et al)
12. Monotonicity of the ratio of modified Bessel functions of the first kind with applications, Journal of Inequalities and Applications, 2018, Article ID:57(with Z. Yang)
13. Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications, Mathematical Inequalities and Applications,21(1)(2018)(with Z. Yang)
14. Sharp Smith’s bounds for the gamma function,Journal of Inequalities and Applications, 2018，Article ID: 27(with X. Li, Z. Liu, Z. Yang) 

2017

1. The monotonicity and convexity for the ratios of modified Bessel functions of the second kind and applications. Proceedings of AMS 145 (2017),no. 7(with Z. Yang)
2. Lorentz estimates for fully nonlinear parabolic and elliptic Equations. Nonlinear Analysis 148 (2017)(with J. Zhang)
3. Uniformly nondegenerate elliptic equations with partially BMO coefficients in nonsmooth domains.Nonlinear Analysis 156 (2017)(with H.Tian) 
4. Complex and Entropy of Fluctuations of Agent-Based Interacting Financial Dynamics with Random Jump. Entropy 2017, 19, 512 (With Y. Wang, W. Zhang and J. Wang)
5. Lorentz estimates for the gradient of weak solutions to elliptic obstacle problems with partially BMO coefficients, Boundary Value Problems, 2017(with H.Tian)
6. Global weighted Lorentz estimates to nonlinear parabolic equations over nonsmooth domains,Journal of Mathematical Analysis and Applications 456 (2017)(H.Tian)
7. Sharp bounds for the ratio of modified Bessel functions, Mediterr. J. Math. (2017) 14:169 (with Z. Yang)
8. New sharp approximations involving incomplete gamma functions, Results in Math.,72( 2017)(with T. Lou, H. Lv, Z.Yang)
9. Lorentz estimates for asymptotically regular fully nonlinear elliptic equations,  Electron. J. Differential Equations, Vol. 2017 (2017), No. 120(Y.Wang and J.Zhang)
10. Sharp inequalities for tangent function with applications.Journal of Inequalities and Applications, 2017, Paper No. 94, 17 pp(with H. Lv, Z.Yang,T. Lou)
11. Weighted Lorentz estimates for nondivergence linear elliptic equations with partially BMO coefficients. Commun. Pure Appl. Anal.16  (2017)  no. 3(with J. Zhang) 

2016

1. Hölder continuity to subelliptic A-harmonic equations under the natural growth.(Chinese) Acta Math. Appl. Sin. 39 (2016), no. 5, 689–700(with H. Yu and J. Wang)
2. Yang, Zhen-Hang; Zheng, Shen-Zhou Monotonicity of a mean related to polygamma functions with an application. J. Inequal. Appl.  2016,  2016:216, 10 pp
3. Sun, Bang-Cheng; Liu, Zhi-Ming; Li, Qiang; Zheng, Shen-Zhou Lp-estimates for quasilinear subelliptic equations with VMO coefficients under the controllable growth. Bound. Value Probl. 2016,2016:148, 18 pp
4. Zhang, Junjie; Zheng, Shenzhou Lorentz estimates for asymptotically regular elliptic equations in quasiconvex domains. Electron. J. Differential Equations 2016, Paper No. 142, 13 pp
5. Sun, Bang-Cheng; Liu, Zhi-Ming; Li, Qiang; Zheng, Shen-Zhou The monotonicity and convexity of a function involving psi function with applications.Journal of Inequalities and Applications,2016, 2016:151,17 pp
6. Zheng, Shenzhou A compactness result for polyharmonic maps in the critical dimension. Czechoslovak Math. J. 66(141) (2016), no.1 
7. Cheng, Cui-Ping; Li, Wan-Tong; Wang, Zhi-Cheng;Zheng, Shenzhou Traveling waves connecting equilibrium and periodic orbit for a delayed population model on a two-dimensional spatial lattice. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 26 (2016), no. 3, 1650049, 13 pp
8. Yu, Haiyan; Zheng, Shenzhou Morrey estimates for subelliptic p-Laplace type systems with VMO coefficients in Carnot groups.Electron. J. Differential Equations 2016, Paper No. 33, 14 pp
9. Zhang, Junjie; Zheng, Shenzhou Lorentz estimate for nonlinear parabolic obstacle problems with asymptotically regular nonlinearities. Nonlinear Analysis 134 (2016) 
10. Yu, Haiyan; Zheng, Shenzhou; Tong, Yuxia An alternative approach to partial regularity of quasilinear elliptic systems with VMO coefficients. J. Inequal. Appl. 2016, 2016:20  

2015

1. Zheng, Shenzhou; Feng, Zhaosheng, Regularity of subelliptic p  -harmonic systems with subcritical growth in Carnot group. J. Differential Equations 258 (2015), no. 7 
2. Zheng, Shenzhou A strong convergence of the weak gradient to A-harmonic type operators with L1 data. Journal of Mathematical Analysis and Applications 430(2015), no.1 
3. Tong, Yu Xia; Zheng, Shen Zhou; Yu, Hai Yan, Local Hölder continuity of the gradients of weak solutions to A-harmonic equation with variable exponents. (Chinese) Acta Math. Sci. Ser. A Chin. Ed. 35 (2015),no.4 
4. Yu, Haiyan; Zheng, Shenzhou, BMO estimate to A-harmonic systems with discontinuous coefficients. Nonlinear Anal. Real World Appl. 26 (2015) 
5. Zheng, Shen Zhou, A local Hölder estimate of (K1,K2)-quasiconformal mappings between hypersurfaces. Acta Math. Sin. (Engl. Ser.)31 (2015), no. 9 
6. Zhang, Jinjie; Zheng, Shenzhou, On refined Hardy-Knopp type inequalities in Orlicz spaces and some related results. J. Inequal. Appl.2015, 2015:169 
7. Yu, Haiyan; Zheng, Shenzhou, Optimal partial regularity for quasilinear elliptic systems with VMO coefficients based on A-harmonic approximations. Electron. J. Differential Equations 2015, No. 16 

2014年以前部分论文:

专著/译著

• 亓健，朱东鸣, 郑神州等. 高等数学（上下册）[M]. 国内:中国石油大学出版社, 2009-03
• 龚漫奇, 邓小琴, 郑神州等. 高等数学习题教程(上、下册）[M]. 科学出版社，2000-12

专利

软件著作权

获奖与荣誉

• 北京市优秀青年骨干教师称号
• 北京市优秀青年论文奖
• "动车组检修计划优化关键技术及应用"获中国铁道学会科技二等奖
• 期刊JMAA-2021年度杰出论文奖(Ames奖)
• 北京交通大学优秀教师
• 北京交通大学课程思政教学名师
  

社会兼职

• 美国数学会《数学评论》（Mathematics Reviews）评论员;
• 国家自然科学基金项目、高等院校科学技术奖、霍英东基金、中国博士后基金、博士点基金、北京市自然科学基金、浙江省自然科学基金等评审专家;  
• 教育部学位办博、硕士学位论文通讯评论专家；
• 专业国际知名期刊Commun. Part. Diff. Equ.,Commun. Nonlinear Sci. Numer. Simulat., JMAA, Science in China等评审专家.