非线性泛函分析、偏微分方程

硕博连读

070101-基础数学

非线性泛函分析
偏微分方程

1988-09--1997-06   山东大学   博士学位

研究生

博士

中国科学院数学与系统科学研究院 二级研究员、博士生导师, 华罗庚数学首席研究员，中国科学院特聘研究员（核心骨干），中国科学院大学岗位教授。国家杰出青年基金获得者、国家“万人计划”领军人才、科技部中青年科技创新领军人才、洪堡学者。

1988年9月-1997年6月，山东大学数学系本科生、研究生，97年6月获得博士学位，1992年获“山东大学优秀毕业生”称号，保送读研究生，曾获山东大学优秀研究生奖、光华奖、阳光工程奖。1997年6月-目前，中国科学院数学与系统科学研究院，历任博士后、助研、副研、研究员(2008.4)。

长期从事非线性泛函分析理论和应用的前沿研究，出版Springer专著一部《Variational, topological, and partial order methods with their applications》，2021.4合著《拓扑与变分方法及应用》由科学出版社出版。在 Journal of Functional Analysis，Annales de l'Institut Henri Poincare Analyse Non Lineaire，J. Differential Equations，Calculus of Variations and PDE, Transactions of the American Mathematical Society等国际著名学术刊物发表论文90多篇，SCI 80多篇。在前沿困难的自由边界问题，Bose-Einstein condensates方程组，生物竞争方程组周期解问题，拟线性椭圆问题，Schrödinger算子的Fučik谱，Monge-Ampere方程，高维波方程，Caffarelli-Kohn-Nirenberg inequalities 相关问题，Kirchhoff 型非局部问题等众多方面取得重要成果, 解决了困难的Terracini猜想和3维Henon-Lane-Emden猜想。这些科研成果产生了广泛的影响，被D.G. Figueiredo院士、Changshou Lin院士、E.N. Dancer院士、Yanyan Li（ICM 45分钟报告人）、 Juncheng Wei（ICM 45分钟报告人）等著名数学家大量引用，Mathematical Reviews(2021.11)显示被1000多名数学家引用2000多次（单篇最高359次），有的已成为基本参考文献，在研究领域起到引领作用。多次应邀在重要国际会议上作大会报告。

多次应邀访问美国、法国、德国、意大利、澳大利亚等国的著名大学，如1999-2000在悉尼大学跟随著名数学家Dancer做博士后，2004-2006年在德国做洪堡学者。

担任国家第二届数学名词审定委员会委员、组长，Springer Nature-Partial Differential Equations and Applications 主编，以及 Boundary Value Problems (SCI，Springer)、 Journal of Nonlinear Functional Analysis等6个国际刊物编委，曾担任钟家庆数学奖评委和中国数学会副秘书长（2012.1-2015.12），哈尔滨工业大学数学研究院学术委员会委员（2016-2021）。担任中组部“青年拔尖人才支持计划”等评审专家，国家基金委及北京市基金通讯评审专家，教育部博士论文评审专家，一些科技奖评审专家。作为国科大岗位教授讲授本科生主要课程“实分析、泛函分析”；已培养博士毕业生16名，博士后4名，有的已成为突出的青年数学人才获得中国数学会钟家庆数学奖、成为万人计划青年拔尖人才。

主持、参加多项国家自然科学（包括重点）基金项目，2011年度获中科院“优秀研究生指导教师奖”，中科院数学与系统科学研究院2011年度十大科研进展， 2013年获北京市科学技术奖，同年获得国家杰出青年基金，2014年入选科技部中青年科技创新领军人才，2016年入选国家“万人计划”领军人才，2017年入选“中国科学院特聘研究员”（核心骨干）和华罗庚数学首席研究员，2020年7月获得“中国科学院优秀党务工作者”称号。

2019-05-29-今,Partial Differential Equations and Applications, 主编
2016-06-29-今,哈尔滨工业大学数学研究院学术委员会, 学术委员会委员
2015-11-01-今,Jounal of Nonlinear Functional Analysis, 编委
2012-05-31-2015-12-31,钟家庆数学奖评审委员会, 评委
2012-03-01-今,全国数学名词委员会委员, 组长
2011-12-28-2015-12-31,中国数学会, 副秘书长
2007-05-17-今,Boundary Value Problems, 编委

本科生毕业设计（数学与应用数学）
泛函分析
非线性分析及对偏微分方程的应用
实分析
科学前沿进展名家系列讲座IV

（1） 极小极大理论及对非线性变分问题的应用, 三等奖, 省级, 2013
（2） 中科院优秀研究生指导教师奖, , 部委级, 2011

   

[1] 张志涛. Yun Zhaoyang, Zhang Zhitao, Normalized solutions to Schrödinger systems with linear and nonlinear couplings,506 ,125564.. J. Math. Anal. Appl.. 2022, [2] 张志涛. Gou Tianxiang, Zhang zhitao, Normalized solutions to the Chern-Simons-Schrodinger system,280,108894. J. Functional Analysis. 2021, [3] 张志涛. Li Kui, Zhang Zhitao, Liouville-type theorem for higher-order Hardy-Henon system, doi: 10.3934/cpaa.2021134. Commun. Pure Appl. Anal.. 2021, [4] 张志涛. Li Zaizheng, Zhang Zhitao, Uniqueness and nondegeneracy of positive solutions to an elliptic system in ecology, doi:10.3934/era.2021060. Electronic research archive. 2021, [5] 张志涛. Cheng Xiyou, Zhang Zhitao, Structure of positive solutions to a class of Schrödinger systems, 14(6),1857–1870.. Discrete Contin. Dyn. Syst. Ser. S,. 2021, [6] 张志涛. Chen Pengyu, Zhang Xuping, Zhang Zhitao, Axymptotic behavior of time periodic solutions for extended Fisher-Kolmogorov Equations with delays,doi:10.3934/dcdsb.2021103. Discrete Contin. Dyn. Syst. Ser. B. 2021, [7] 张志涛. Huang Shuibo, Zhang Zhitao, ZhisuLiu, Qualitative properties of singular solutions to fractional elliptic equations, DOI:10.1017/prm.2021.52. Proceedings of the Royal Society of Edinburgh. 2021, [8] 张志涛. Chen Jianyi, Zhang Zhitao, Chang Guijuan, Zhao Jing,Periodic Solutions to Klein–Gordon Systems with Linear Couplings. Adv. Nonlinear Stud.. 2021, [9] 张志涛. Zhang Xinqiu, Zhang Zhitao, Distribution of positive solutions to Schrödinger systems with linear and nonlinear couplings.. J. Fixed Point Theory Appl.. 2020, [10] 张志涛. Dai Guowei, Sun Yimin, Wang Zhi-Qiang, Zhang Zhitao,The structure of positive solutions for a Schrödinger system. Topol. Methods Nonlinear Anal. 2020, [11] 张志涛. Haijun Luo, Zhitao Zhang, Normalized solutions to the fractional Schrödinger equations with combined nonlinearities. Calc. Var. Partial Differential Equations. 2020, [12] 张志涛. Sun Jingxian, Pan Xingbin, Du Yihong, Liu Zhaoli, Zhang Zhitao, Professor Dajun Guo: a true mathematician and educator. SN Partial Differential Equations and Applications. 2020, [13] 张志涛. Luo Haijun, Zhang Zhitao,Existence of positive solutions to Kirchhoff equations with vanishing potentials and general nonlinearity. SN Partial Differential Equations and Applications. 2020, [14] 张志涛. Sun Dongdong, Zhang Zhitao, Existence of positive solutions to Kirchhoff equations with vanishing potentials and general nonlinearity. SN Partial Differential Equations and Applications. 2020, [15] 张志涛. Dai, Guowei; Tian, Rushun; Zhang, Zhitao Global bifurcations and a priori bounds of positive solutions for coupled nonlinear Schrödinger systems.. Discrete Contin. Dyn. Syst. Ser. S. 2019, [16] 张志涛. Lou, Zhenluo; Weth, Tobias; Zhang, Zhitao Symmetry breaking via Morse index for equations and systems of Hénon-Schrödinger type.. Z. Angew. Math. Phys.. 2019, [17] 张志涛. Zhisu Liu, Zhitao Zhang, Shuibo Huang, Existence and nonexistence of positive solutions for a static Schrodinger-Poisson-Slater Equation,. J. Differential Equations, https://doi.org/10.1016/j.jde.2018.10.048. 2019, [18] 张志涛. Liu, Zhisu; Luo, Haijun; Zhang, Zhitao Dancer-Fučik spectrum for fractional Schrödinger operators with a steep potential well on RN.. Nonlinear Anal.. 2019, [19] 张志涛. Kui Li , Zhitao Zhang, Proof of the Hénon–Lane–Emden conjecture in R3 , https://doi.org/10.1016/j.jde.2018.07.036. J. Differential Equations,. 2019, [20] 张志涛. Sun, Dongdong; Zhang, Zhitao Existence and asymptotic behaviour of ground state solutions for Kirchhoff-type equations with vanishing potentials.. Z. Angew. Math. Phys.. 2019, [21] 张志涛. Luo, Haijun; Zhang, Zhitao Existence and nonexistence of bound state solutions for Schrödinger systems with linear and nonlinear couplings.. J. Math. Anal. Appl.. 2019, [22] 张志涛. Kui Li, Zhitao Zhang,Foliated Schwarz symmetry for the nodal solution at second minimax level.. Annali di Matematica Pura ed Applicata (4) 197 (2018), no. 6, 1875–1883,. 2018, [23] 张志涛. Dongdong Sun, Zhitao Zhang,Uniqueness, existence and concentration of positive ground state solutions for Kirchhoff type problems in R^3, Vol. 461, No.1,128-149,(2018). J. Math. Appl. Anal.. 2018, [24] 张志涛. K. Perera, Cyril Tintarev, Jun Wang, Zhitao Zhang, Ground and bound state solutions for a Schrödinger system with linear and nonlinear couplings in , 23 (2018), no. 7-8, 615–648.. Advances in Differential Equations. 2018, [25] 张志涛. Zhitao Zhang, Haijun Luo, Symmetry and Asymptotic Behavior of Ground State Solutions for Schrodinger Systems with Linear Interaction,. Communications on Pure and Applied Analysis,17 (2018), no. 3, 787–806.. 2018, [26] 张志涛. Kanishka Perera, Yang Yang, Zhitao Zhang, Asymmetric critical p-Laplacian problems.. Calc. Var. Partial Differential Equations 57 (2018), no. 5, Art. 131, 18 pp.. 2018, [27] 张志涛. Zongming Guo, Linfeng Mei, Zhitao Zhang, Morse index and symmetry breaking for an elliptic equation with negative exponent in expanding annuli. Proceedings of the Royal Society of Edinburgh,147A，1215-1232. 2017, [28] 张志涛. Jianyi Chen, Zhitao Zhang, Existence of multiple periodic solutions to asymptotically linear wave equations in a ball. Calc. Var. Partial Differential Equations,56(3), Art 58, 25 pages. 2017, [29] 张志涛. Zhitao Zhang, Wei Wang, Structure of positive solutions to a Schrödinger system(2017). J. Fixed Point Theory Appl. 19,877-887.. 2017, [30] Zhang, Zhitao, Sun, Yimin. Existence and Multiplicity of Solutions for Nonlocal Systems with Kirchhoff Type. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES[J]. 2016, 32(1): 35-54, https://www.webofscience.com/wos/woscc/full-record/WOS:000373403700003.
[31] 张志涛. Kui Li, Zhitao Zhang, Existence of solutions for a Schrödinger system with linear and nonlinear couplings.. J. Math. Phys.,57,081504. 2016, [32] Chen, Jianyi, Zhang, Zhitao. Existence of infinitely many periodic solutions for the radially symmetric wave equation with resonance. JOURNAL OF DIFFERENTIAL EQUATIONS[J]. 2016, 260(7): 6017-6037, http://dx.doi.org/10.1016/j.jde.2015.12.026.
[33] Tian RuShun, Zhang ZhiTao. Existence and bifurcation of solutions for a double coupled system of Schrodinger equations. SCIENCE CHINA-MATHEMATICS[J]. 2015, 58(8): 1607-1620, http://ir.amss.ac.cn/handle/2S8OKBNM/46363, http://www.irgrid.ac.cn/handle/1471x/6869196, http://ir.amss.ac.cn/handle/2S8OKBNM/46364.
[34] Chen, Jianyi, Zhang, Zhitao. Infinitely many periodic solutions for a semilinear wave equation in a ball in R-n. JOURNAL OF DIFFERENTIAL EQUATIONS[J]. 2014, 256(4): 1718-1734, https://www.webofscience.com/wos/woscc/full-record/WOS:000330204600015.
[35] 张志涛. Addendum to The limit equation for the Gross-Pitaevskii equations and S. Terracini conjecture. 2013, [36] Dancer, E N, Wang, Kelei, Zhang, Zhitao. The limit equation for the Gross-Pitaevskii equations and S. Terracini's conjecture. JOURNAL OF FUNCTIONAL ANALYSIS[J]. 2012, 262(3): 1087-1131, http://dx.doi.org/10.1016/j.jfa.2011.10.013.
[37] Dancer, E N, Wang, Kelei, Zhang, Zhitao. DYNAMICS OF STRONGLY COMPETING SYSTEMS WITH MANY SPECIES. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY[J]. 2012, 364(2): 961-1005, https://www.webofscience.com/wos/woscc/full-record/WOS:000300137200017.
[38] Dancer, E N, Wang, Kelei, Zhang, Zhitao. Uniform Holder estimate for singularly perturbed parabolic systems of Bose-Einstein condensates and competing species. JOURNAL OF DIFFERENTIAL EQUATIONS[J]. 2011, 251(10): 2737-2769, https://www.webofscience.com/wos/woscc/full-record/WOS:000294835800004.
[39] Cheng XiYou, Zhang ZhiTao. Positive solutions for a multi-parameter system of second-order ordinary differential equations. SCIENCE CHINA-MATHEMATICS[J]. 2011, 54(5): 959-972, https://www.webofscience.com/wos/woscc/full-record/WOS:000290768800008.
[40] Wang, Kelei, Zhang, Zhitao. Some new results in competing systems with many species. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE[J]. 2010, 27(2): 739-761, http://dx.doi.org/10.1016/j.anihpc.2009.11.004.
[41] Bartsch, Thomas, Wang, ZhiQiang, Zhang, Zhitao. On the Fucik point spectrum for Schrodinger operators on R-N. JOURNAL OF FIXED POINT THEORY AND APPLICATIONS[J]. 2009, 5(2): 305-317, https://www.webofscience.com/wos/woscc/full-record/WOS:000268726400007.
[42] Zhitao Zhang, Kelei Wang. Existence and non-existence of solutions for a class of Monge–Ampère equations. Journal of Differential Equations. 2009, 2849-2875, http://dx.doi.org/10.1016/j.jde.2009.01.004.
[43] Bartsch, Thomas, Peng, Shuangjie, Zhang, Zhitao. Existence and non-existence of solutions to elliptic equations related to the Caffarelli-Kohn-Nirenberg inequalities. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS[J]. 2007, 30(1): 113-136, https://www.webofscience.com/wos/woscc/full-record/WOS:000247271800005.
[44] Perera, K, Zhang, ZT. Nontrivial solutions of Kirchhoff-type problems via the Yang index. JOURNAL OF DIFFERENTIAL EQUATIONS[J]. 2006, 221(1): 246-255, http://dx.doi.org/10.1016/j.jde.2005.03.006.
[45] 张志涛. Elliptic equations in $\Bbb R^2$ with one-sided exponential growth. Commun. Contemp. Math.. 2004, [46] 张志涛. Construction of pseudo-gradient vector field and sign-changing multiple solutions involving $p$p-Laplacian.. J. Differential Equations. 2004, [47] Zhang, ZT, Li, SJ. On sign-changing and multiple solutions of the p-Laplacian. JOURNAL OF FUNCTIONAL ANALYSIS[J]. 2003, 197(2): 447-468, http://dx.doi.org/10.1016/S0022-1236(02)00103-9.
[48] Zhang, ZT, Li, XD. Sign-changing solutions and multiple solutions theorems for semilinear elliptic boundary value problems with a reaction term nonzero at zero. JOURNAL OF DIFFERENTIAL EQUATIONS[J]. 2002, 178(2): 298-313, http://dx.doi.org/10.1006/jdeq.2001.4015.
[49] Dancer, EN, Zhang, ZT. Dynamics of Lotka-Volterra competition systems with large interaction. JOURNAL OF DIFFERENTIAL EQUATIONS[J]. 2002, 182(2): 470-489, http://dx.doi.org/10.1006/jdeq.2001.4102.
[50] Shujie Li, Zhitao Zhang. Fucik spectrum, sign-changing and multiple solutions for semilinear elliptic boundary value problems with jumping nonlinearities at zero and infinity. Science in China Series. 2001, 44(7): http://kns.cnki.net/KCMS/detail/detail.aspx?QueryID=0&CurRec=1&recid=&FileName=SSJD00000031773&DbName=SSJD_01&DbCode=SSJD&yx=&pr=&URLID=&bsm=.

（1） Zhitao Zhang, Variational,topological and partial order methods with their applications, Springer, 2013-01, 第 1 作者
（2） 李树杰 张志涛，拓扑与变分方法及应用, Topological and Variational Methods and Applications, 科学出版社, 2021-04, 第 2 作者

   

（ 1 ） 变分方法与非线性微分方程前沿问题, 主持, 国家级, 2013-01--2016-12
（ 2 ） 中科院数学院七大重点培育方向课题, 参与, 部委级, 2012-01--2015-12
（ 3 ） 非线性泛函分析(国家杰出青年基金), 主持, 国家级, 2014-01--2017-12
（ 4 ） 国家万人计划, 主持, 国家级, 2017-01--2019-12
（ 5 ） 变分方法与非线性偏微分方程若干前沿问题研究, 主持, 国家级, 2018-01--2021-12
（ 6 ） 拟线性椭圆方程的多解研究, 主持, 国家级, 2020-01--2020-12
（ 7 ） 现代变分理论的若干前沿课题, 参与, 国家级, 2021-01--2025-10
（ 8 ） 拟线性Schrodinger方程和非局部Kirchhoff问题研究, 主持, 国家级, 2021-01--2021-12

（1）Existence of solutions for Schrodinger systems with linear and nonlinear couplings   第六届偏微分方程及其应用学术论坛   2021-09-25
（2）Existence of solutions for Schrodinger systems with linear and nonlinear couplings   2021-06-24
（3）Normalized solutions to the Chern-Simons-Schrodinger system   动力系统与非线性分析研讨会   2021-05-21
（4）Normalized solutions to the Chern-Simons-Schrodinger system and fractional Schrodinger equations   偏微分方程与几何分析会议   2021-05-17
（5）Normalized solutions to the Chern-Simons-Schrodinger system and fractional Schrodinger equations   变分与椭圆型偏微分方程学术研讨会   2021-05-14
（6）Normalized solutions to the fractional Schrodinger equations with combined nonlinearities   西北微分方程及应用学术会议   2020-09-26
（7）Henon-Lane-Emden conjecture and related Schrodinger systems   非线性泛函分析及其应用研讨会   2020-06-27
（8）Existence of solutions for Schrodinger systems with linear and nonlinear couplings   第五届偏微分方程及其应用学术论坛   2020-05-23
（9）Some new results on Henon-Lane-Emden conjecture and Schrodinger systems   中日青年数学家非线性偏微分方程研讨会（Japan）   2018-10-26
（10）Some new results on Henon-Lane-Emden conjecture and Schrodinger systems   偏微分方程与物理学、生物学交叉学科论坛   2018-09-21
（11）Some new results on Henon-Lane-Emden conjecture and Schrodinger systems    第十二届AIMS动力系统和微分方程及应用国际会议   2018-07-05
（12）Some new results on Henon-Lane-Emden conjecture and Schrodinger systems   非线性泛函分析及应用学术会议   2018-06-22
（13）Some new results on Henon-Lane-Emden conjecture and Schrodinger systems   变分方法和拓扑方法及应用国际会议，USA   2018-06-05
（14）Some new results on Schrodinger systems   偏微分方程学术研讨会   2018-04-21
（15）On the Henon-Lane-Emden conjecture in R^3   偏微分方程及其应用学术论坛   2017-11-18
（16）On solutions of Schrodinger systems arising from Bose-Einstein condensates   第九届全国算子理论与算子代数会议   2017-10-28
（17）Existence of solutions for Schrodinger systems with linear and nonlinear couplings   2017-06-12
（18）Existence of solutions for Schrodinger systems with linear and nonlinear couplings   偏微分方程和非线性国际学术会议   2017-04-21
（19）Existence and bifurcation of solutions for Schrodinger systems   Zhitao Zhang   2016-06-13
（20）Existence, uniqueness, and bifurcation of solutions for Schr\"{o}dinger systems   Zhitao Zhang   2016-05-29
（21）Existence and bifurcation of solutions for systems of Schrodinger equations   张志涛   2015-12-18
（22）Existence of solution for system of Schrodinger equations   Zhitao Zhang   2015-08-10
（23）Some new results on systems of nonlinear differential equations   Zhitao Zhang   2014-05-20
（24）Free boundary problems and BEC equations   Zhitao Zhang   2012-06-19
（25）Free boundary problems   边值问题、积分方程以及相关问题   Zhitao Zhang   2010-08-25
（26）Free boundary problems and competing systems with many species   泛函分析及其应用国际学术研讨会   Zhitao Zhang   2010-07-25

已指导学生

王克磊  博士研究生  070101-基础数学  

张齐  硕士研究生  070101-基础数学  

孙宜民  博士研究生  070101-基础数学  

颜晓琳  博士研究生  070101-基础数学  

陈建毅  博士研究生  070101-基础数学  

齐泽心  博士研究生  070101-基础数学  

丁素丽  硕士研究生  070101-基础数学  

娄振洛  博士研究生  070101-基础数学  

李奎  博士研究生  070101-基础数学  

孙冬冬  博士研究生  070101-基础数学  

王威  博士研究生  070101-基础数学  

罗海军  博士研究生  070101-基础数学  

郑晓甜  博士研究生  070101-基础数学  

于萌  硕士研究生  070101-基础数学  

李再铮  博士研究生  070101-基础数学  

李京谕  硕士研究生  070101-基础数学  

现指导学生

秦俭  博士研究生  070101-基础数学  

张伟俊  博士研究生  070101-基础数学  

张泽鑫  博士研究生  070101-基础数学  

员兆阳  博士研究生  070101-基础数学  

于萌  博士研究生  070101-基础数学  

邓崇昊  硕士研究生  070101-基础数学  

高静  博士研究生  070101-基础数学  

郝慧琴  博士研究生  070101-基础数学  

裴文梁  博士研究生  070101-基础数学