贺小明

发布日期:2019-10-10    浏览次数:

 

基本情况: 贺小明,湖南溆浦人,瑶族,理学博士,教授,研究生导师,中央民族大学应用数学研究所所长。

主要经历:1999年毕业于湖南大学应用数学系,获硕士学位,导师黄立宏教授。2002年毕业于北京理工大学,获博士学位,导师葛渭高教授。2002-2004年在中科院应用数学研究所做博士后,导师曹道民研究员。2004年秋季进入中央民族大学数学与计算机学院工作至今。在此期间,2006-2008年在清华大学数学系做在职博士后,导师邹文明教授。

研究领域: 1,非线性泛函分析及应用 2,微分方程理论及应用。

教学工作:讲授过本科生的泛函分析、实变函数、数学分析、复变函数、数学物理方程、常微分方程、数学文化等课程;研究生的拓扑学、二阶椭圆型方程、非线性泛函分析等课程。出版教材两部。

1,贺小明,赵志红,张学梅,数学物理方程,中央民族大学出版社,2011年。

2,贺小明,彭名书,常微分方程与动力系统概论,北京理工大学出版社,2010年。

科研工作: 发表科研论文50余篇,专著1部,其中ESI高被引论文2篇。

[1]He, Xiaoming; Zou, Wenming,Ground state solutions for a class of fractional Kirchhoff equations with critical growth, Science China Mathematics,62(2019),853–890. (SCI)

[2]J. M. do O,Xiaoming He ,P. K. Mishra,Fractional Kirchhoff problem with critical indefinite nonlinearity, Mathematische Nachrichten,292(2019),615-632. (SCI)

[3]He, Xiaoming; Zou, Wenming, Multiplicity of concentrating solutions for a class of fractional Kirchhoff equation,Manuscript Math, 158(2019),159–203. (SCI)

[4]Fengqin Lan,Xiaoming He,The Nehari manifold for a fractional critical Choquard equation involving sign-changing weight functions,Nonlinear Anal. 180 (2019), 236-263. (SCI)

[5]Xiaotian Han, Xiaoyan Ma & Xiaoming He,Existence of sign-changing solutions for a class of p-Laplacian Kirchhoff-type equations,Complex Variables and Elliptic Equations,64(2019),181-203. (SCI)

[6] He, Xiaoming; Zou, Wenming, Multiplicity of concentrating positive solutions for Schrödinger-Poisson equations with critical growth. Nonlinear Anal. 170 (2018), 142–170. (SCI)

[7] Guo, Qing; He, Xiaoming, Semiclassical states for weakly coupled fractional Schrödinger systems. J. Differential Equations 263 (2017), no. 4, 1986–2023. (SCI)

[8] Guo, Qing; He, Xiaoming, Semiclassical states for fractional Schrödinger equations with critical growth. Nonlinear Anal. 151 (2017), 164–186. (SCI)

[9] Jiao, Hai Tao; Ma, Xiao Yan; Guo, Qing; He, Xiao Ming, Existence of least energy sign-changing solutions for a Schrödinger-Poisson equation with potential vanishing at infinity. (Chinese) Acta Math. Appl. Sin. 39 (2016), no. 6, 897–916. (核心期刊)

[10] He, Xiaoming; Zou, Wenming, Existence and concentration result for the fractional Schrödinger equations with critical nonlinearities. Calc. Var. Partial Differential Equations 55 (2016), no. 4, Art. 91, 39 pp. (SCI)

[11] He, Xiaoming; Squassina, Marco; Zou, Wenming, The Nehari manifold for fractional systems involving critical nonlinearities. Commun. Pure Appl. Anal. 15 (2016), no. 4, 1285–1308. (SCI)

[12] Ba, Zhen; He, Xiaoming, Solutions for a class of Schrödinger-Poisson system in bounded domains. J. Appl. Math. Comput. 51 (2016), no. 1-2, 287–297. (EI)

[13] Ma, Xiaoyan; He, Xiaoming, Nontrivial solutions for Kirchhoff equations with periodic potentials. Electron. J. Differential Equations 2016, Paper No. 102, 22 pp. (SCI)

[14] Guo, Qing; He, Xiaoming, Least energy solutions for a weakly coupled fractional Schrödinger system. Nonlinear Anal. 132 (2016), 141–159. (SCI)

[15] He, Xiaoming, Multiplicity of solutions for a nonlinear Klein-Gordon-Maxwell system. Acta Appl. Math. 130 (2014), 237–250. (SCI)

[16] He, Xiaoming; Zou, Wenming, Ground states for nonlinear Kirchhoff equations with critical growth. Ann. Mat. Pura Appl. (4) 193 (2014), no. 2, 473–500. (SCI)

[17] He, Xiaoming; Qian, Aixia; Zou, Wenming, Existence and concentration of positive solutions for quasilinear Schrödinger equations with critical growth. Nonlinearity 26 (2013), no. 12, 3137–3168. (SCI)

[18] He, Xiaoming; Zou, Wenming, Existence and concentration of ground states for Schrödinger-Poisson equations with critical growth. J. Math. Phys. 53 (2012), no. 2, 023702, 19 pp. (SCI)

[19] Liu, Wei; He, Xiaoming, Multiplicity of high energy solutions for superlinear Kirchhoff equations. J. Appl. Math. Comput. 39 (2012), no. 1-2, 473–487. (EI)

[20] He, Xiaoming; Zou, Wenming, Existence and concentration behavior of positive solutions for a Kirchhoff equation in R^3. J. Differential Equations 252 (2012), no. 2, 1813–1834. (SCI)

[21] He, Xiaoming, Multiplicity and concentration of positive solutions for the Schrödinger-Poisson equations. Z. Angew. Math. Phys. 62 (2011), no. 5, 869–889. (SCI)

[22]贺小明,一类具临界指数增长的Schrodinger-Poisson系统正解的多重性,中国科学 数学,7(2011),577-600. (核心期刊)

[23] He, Xiaoming; Zou, Wenming, Infinitely many solutions for a singular elliptic equation involving critical Sobolev-Hardy exponents in R^N. Acta Math. Sci. Ser. B (Engl. Ed.) 30 (2010), no. 3, 830–840. (SCI)

[24] He, Xiao-ming; Zou, Wen-ming, Multiplicity of solutions for a class of Kirchhoff type problems. Acta Math. Appl. Sin. Engl. Ser. 26 (2010), no. 3, 387–394. (SCI)

[25] He, Xiaoming, Multiple radial solutions for a class of quasilinear elliptic problems. Appl. Math. Lett. 23 (2010), no. 1, 110–114. (SCI)

[26] He, Xiaoming; Zou, Wenming, Existence and multiplicity of solutions for an elliptic system with nonlinear boundary conditions. Nonlinear Anal. 71 (2009), no. 10, 4646–4656. (SCI)

[27]He, Xiaoming; Zou, Wenming, Multiplicity of solutions for a class of elliptic boundary value problems. Nonlinear Anal. 71 (2009), no. 7-8, 2606–2613. (SCI)

[28]Wang, Yuqing; He, Xiaoming, A note on a nonlinear functional differential system with feedback control. Electron. J. Qual. Theory Differ. Equ. 2009, No. 13, 9 pp. (SCI)

[29] He, Xiaoming; Zou, Wenming, Infinitely many arbitrarily small solutions for singular elliptic problems with critical Sobolev-Hardy exponents. Proc. Edinb. Math. Soc. (2) 52 (2009), no. 1, 97–108. (SCI)

[30] He, Xiaoming; Zou, Wenming, Infinitely many positive solutions for Kirchhoff-type problems. Nonlinear Anal. 70 (2009), no. 3, 1407–1414. (SCI)

[31] He, Xiaoming; Zou, Wenming, Multiple solutions for the Brezis-Nirenberg problem with a Hardy potential and singular coefficients. Comput. Math. Appl. 56 (2008), no. 4, 1025–1031. (SCI)

[32] He, Xiaoming; Zou, Wenming, Multiplicity of solutions for quasilinear Brezis-Nirenberg type problems involving singular weights. Int. J. Pure Appl. Math. 44 (2008), no. 4, 493–507.

[33] He, Xiaoming; Zou, Wenming, Nontrivial solutions for some singular critical growth semilinear elliptic equations. Nonlinear Anal. 68 (2008), no. 12, 3719–3732. (SCI)

[34] He, Xiaoming; Zou, Wenming, Nontrivial solitary waves to the generalized Kadomtsev-Petviashvili equations. Appl. Math. Comput. 197 (2008), no. 2, 858–863. (SCI)

[35] Cao, Daomin; He, Xiaoming; Peng, Shuangjie, Positive solutions for some singular critical growth nonlinear elliptic equations. Nonlinear Anal. 60 (2005), no. 3, 589–609. (SCI)

[36] He, Zhimin; He, Xiaoming, Monotone iterative technique for impulsive integro-differential equations with periodic boundary conditions. Comput. Math. Appl. 48 (2004), no. 1-2, 73–84. (SCI)

[37] He, Xiaoming, Double positive solutions of a three-point boundary value problem for the one-dimensional p-Laplacian. Appl. Math. Lett. 17 (2004), no. 8, 867–873. (SCI)

[38] He, Zhimin; He, Xiaoming, Periodic boundary value problems for first order impulsive integro-differential equations of mixed type. J. Math. Anal. Appl. 296 (2004), no. 1, 8–20. (SCI)

[39] He, Xiaoming; Ge, Weigao, Twin positive solutions for the one-dimensional p-Laplacian boundary value problems. Nonlinear Anal. 56 (2004), no. 7, 975–984. (SCI)

[40] He, Xiao Ming; Ge, Wei Gao, A theorem about triple positive solutions for the one-dimensional p-Laplacian equations. (Chinese) Acta Math. Appl. Sin. 26 (2003), no. 3, 504–510. (核心期刊)

[41] He, Xiao Ming; Ge, Wei Gao, Existence of positive solutions for the one-dimensional p-Laplacian equations. (Chinese) Acta Math. Sinica (Chin. Ser.) 46 (2003), no. 4, 805–810. (核心期刊)

[42] He, Xiaoming; Ge, Weigao, Positive solutions for semipositone (n,p) boundary value problems. Port. Math. (N.S.) 60 (2003), no. 3, 253–262. (SCI)

[43] He, Xiaoming; Ge, Weigao, Existence of three solutions for a quasilinear two-point boundary value problem. Comput. Math. Appl. 45 (2003), no. 4-5, 765–769. (SCI)

[44] He, Xiaoming; Ge, Weigao, Positive solutions for semipositone (k,n-k) boundary value problems. Indian J. Pure Appl. Math. 33 (2002), no. 9, 1361–1371. (SCI)

[45] He, Xiaoming; Ge, Weigao, Positive solutions for semipositone (p,n-p) right focal boundary value problems. Appl. Anal. 81 (2002), no. 2, 227–240. (SCI)

[46] He, Xiaoming; Ge, Weigao, Positive solutions and nonlinear eigenvalue problem of one-dimensional p-Laplacian FDE. Appl. Anal. 81 (2002), no. 1, 115–128. (SCI)

[47] He, Xiao-ming; Ge, Wei-gao, Existence of multiple positive solutions for higher-order p-Laplacian boundary value problems. J. Beijing Inst. Tech. (Engl. Ed.) 11 (2002), no. 2, 212–216. (EI)

[48] He, Xiaoming; Ge, Weigao; Peng, Mingshu, Multiple positive solutions for one-dimensional p-Laplacian boundary value problems. Appl. Math. Lett. 15 (2002), no. 8, 937–943. (SCI)

[49] He, Xiaoming; Ge, Weigao; He, Zhimin, First-order impulsive functional differential equations with periodic boundary value conditions. Indian J. Pure Appl. Math. 33 (2002), no. 8, 1257–1273. (SCI)

[50] Xiaoming, H.; Weigao, G., A remark on some three-point boundary value problems for the one-dimensional p-Laplacian. ZAMM Z. Angew. Math. Mech. 82 (2002), no. 10, 728–731. (SCI)

[51] He, Xiaoming; Ge, Weigao, Triple solutions for second-order three-point boundary value problems. J. Math. Anal. Appl. 268 (2002), no. 1, 256–265. (SCI)

[52]贺小明,Applications of Variational Methods,中央民族大学出版社,2010年。


论文引用情况:据美国“数学评论”数据库记录(MathSciNet)

(https://www.ams.org):已发表论文被600多位作者SCI引用1000多篇次,平均每篇引用20多篇次。


主持和参加的科研项目

1,国家自然科学基金面上项目(11771468):几类分数阶非局部椭圆型方程的变分问题研究,48万,2018-2021。主持。

2,国家自然科学基金面上项目(11271386):变分与拓扑方法对若干重要椭圆方程的应用研究,60万,2013-2016。主持。

3,国家自然科学基金面上项目(10971238):临界点理论及其应用方面的一些新问题研究,26万,2010-2012。主持。

4,国家自然科学基金面上项目(11971027):不可微泛函与Orlicz闵可夫斯基问题,2020-2023。48万,参加。

5,国家自然科学基金面上项目(11371212):与Bose-Einstein凝聚方程相关的非线性椭圆系统的研究,2014-2017。60万,参加。

6,国家自然科学基金面上项目(11171341):非线性负指数椭圆型方程,2012-2015。24万,参加。

72006年第39批中国博士后科学基金,编号:20060390075, 主持。

82002年第32批中国博士后科学基金,主持。

92006年中央民族大学“青年教师”科研基金资助项目,拟线性型及离散型Hamilton系统变分问题研究,编号:CUN 0219,主持。

102009年中央民族大学自主科研项目,脉冲微分方程理论在少数民族地区生态系统中的应用研究,编号:0910KYZ51, 主持。

获奖情况和人才计划:

1, 获北京理工大学优秀博士学位论文奖(2002年)。

2, 获中国科学院王宽诚博士后工作奖励基金(2002年)。

3, 获2012年中央民族大学优秀教学成果二等奖 (独立完成,2012年)。

4,入选中央民族大学“高层次优秀人才”支持计划(2016-2019年)。

学术交流:

12009.2-2010.1:公派访学美国犹他州立大学数学与统计系(Utah State University),访问学者。

2, 2018.10-2018.11,德国曼汉姆大学 数学系(University of Mannheim),访问学者。

3,2019.7-2019.8,德国弗莱堡大学 数学系(Albert-Ludwigs-Universität Freiburg),访问学者。

社会服务:

1,国内外30多种数学期刊,含JDE;Calc. Var. PDE; JMAA; Nonlinear Anal.(RWA);ZAMP;Nodea; Nonlinearity; J. Math. Phys.; Appl. Math. Lett.; CMA.; CPAA; DCDS;EJDE;ANA;ANS;AA;CVEE等期刊在内的审稿人。

2,霍英东基金青年教师奖、国家自然科学基金等项目通讯评审专家。

办公地点:中央民族大学理工楼817-2

电子邮件xmhe923@muc.edu.cn

电话:010-68932822(转821)