东北师范大学数学与统计学院
个人信息
School of Mathematics and Statistics,NENU
Personal Particulars
常小军  教授
【基本信息】
性    别
办公地点数统楼210室
职    称教授
电子邮箱changxj100@nenu.edu.cn
专    业基础数学
个人主页常小军
【个人情况综述】
常小军,教授,博士生导师, 第七届教授委员会委员,主要从事非线性分析和动力系统的研究。已在《Annales de l’Institut Henri Poincaré, Analyse Non Linéaire.》, 《Trans. Amer. Math.Soc.》,《J. Differential Equations》,《Nonlinearity》,《 J. Geom. Anal.》,《Commun. Contemp. Math.》等国际专业期刊上发表论文三十余篇。主持国家自然科学基金面上项目(2项)与省部级项目多项,任吉林省工业与应用数学学会常务理事。
【学习工作简历】

2004.9-2009.6  吉林大学数学研究所  硕士,博士
2000.9-2004.6  吉林大学数学学院     本科

2010.3--2012.3  南开大学陈省身数学研究所  博士后

2009.7-2012.9   吉林大学数学学院, 讲师

2012.9—         吉林大学数学学院,副教授
2015.1至今 东北师范大学数学与统计学院  教授


2016.8-2017.9, 美国犹他州立大学数学系,   访问学者
2018.8-2018.11  日本早稻田大学数学系,    访问学者
2019.8-2019.11,2021.12-2022.12  法国佛朗什-孔泰大学数学系,访问学者
2020.1-2020.2   日本琦玉大学数学系,      访问学者

【社会学术兼职】
美国数学会《Mathematical Review》评论员, 吉林省工业与应用数学学会常务理事,国家自然科学基金委员会同行评议专家, 教育部抽检博士学位论文通讯评议专家。
【获奖情况】
1.吉林省自然科学学术成果奖三等奖,2014年,排名第1。
2.吉林省自然科学学术成果奖三等奖,2015年,排名第2。
【主要研究方向】

主要应用变分与拓扑方法研究非线性(非局部)薛定谔方程(组)解的存在性、多重性,解的集中等。

近期感兴趣的领域:

1. 图上的变分方法及其应用(度量图、离散图)。

2.各种非线性薛定谔方程(组)的正规化解问题。


代表作如下:


1. J. Borthwick, X. J. Chang, L. Jeanjean and N. Soave,  Bounded Palais-Smale sequences with Morse type information for some constrained functionals, Trans. Amer. Math. Soc., Online, DOI: 10.1090/tran/9145.

2. X. J. Chang, L. Jeanjean and N. Soave, Normalized solutions of $L^2$-supercritical NLS equations on compact metric graphs, Annales de l Institut Henri Poincare (C) Non Linear Analysis, Online, DOI: 10.4171/AIHPC/88.

3.X. J. Chang, Y. Sato and Chengxiang, Zhang, Multi-peak solutions of a class of fractional p-Laplacian equations,J. Geom. Anal. 34(2024), no. 1,  Paper No. 29, 36 pp.

4. J. Borthwick, X. J. Chang, L. Jeanjean and N. Soave,  Normalized solutions of $L^2$-supercritical NLS equations on noncompact metric graphs with localized nonlinearities,  Nonlinearity. 36(2023) 3776-3795.

5. X. J. Chang, R. Wang and D. K. Yan, Ground states for logarithmic Schrödinger equations on locally finite graphs.  J. Geom. Anal. 33 (2023), no. 7, Paper No. 211, 26 pp.
6. X. J. Chang,  M. T. Liu and D. K. Yan, Normalized ground state solutions of nonlinear Schrödinger equations involving exponential critical growth.  J. Geom. Anal. 33 (2023), no. 3, Paper No. 83, 20 pp.

7. X. J. Chang and W. Sun, Existence of least energy nodal solutions for a double-phase problem with nonlocal nonlinearity. App. Anal. 102 (2023), no. 6, 1752–1764.

8. X. J. Chang, V. D. Radulescu, R. Wang and D. K. Yan, Convergence of least energy sign-changing solutions for logarithmic Schrodinger equations on locally finite graphs, Commun. Nonlinear Sci. Numer. Simul. 125(2023) Paper No. 107418, 19 pp.

9. Yuxin Li, X. J. Chang and Z. S. Feng, Normalized solutions for Sobolev critical Schrodinger-Bopp-Podolsky systems, Elec. J. Differential Equations, Vol. 2023 (2023), No. 56, pp. 1–19.

10. X. J. Chang and Y. Sato, Multiplicity of localized solutions of nonlinear Schrödinger systems for infinite attractive case. J. Math. Anal. Appl. 491 (2020), no. 2, 124358, 17 pp.

11. X. J. Chang and  Y. Sato, Localized solutions of nonlinear Schrödinger systems with critical frequency for infinite attractive case. NoDEA Nonlinear Differential Equations Appl. 26 (2019), no. 5, Paper No. 31, 31 pp.

12. X. J. Chang, Z. H. Nie and Z.-Q. Wang, Sign-changing solutions of fractional p-Laplacian problems.
Adv. Nonlinear Stud. 19 (2019), no. 1, 29–53.

13.X. J. Chang, T. C. Ouyang and D. K. Yan, Linear stability of the criss-cross orbit in the equal-mass three-body problem. Discrete Contin. Dyn. Syst. 36 (2016), no. 11, 5971–5991.

14. X. J. Chang and Y. Li, Rotating periodic solutions of second order dissipative dynamical systems. Discrete Contin. Dyn. Syst. 36 (2016), no. 2, 643–652.

15. X. J. Chang, Ground states of some fractional Schrödinger equations on RN. Proc. Edinb. Math. Soc. (2) 58 (2015), no. 2, 305–32.

16. X. J. Chang and Z.-Q. Wang, Nodal and multiple solutions of nonlinear problems involving the fractional Laplacian. J. Differential Equations 256 (2014), no. 8, 2965–2992.

17. X. J. Chang, Ground state solutions of asymptotically linear fractional Schrödinger equations. J. Math. Phys. 54 (2013), no. 6, 061504, 10 pp.

18. X. J. Chang and Z.-Q. Wang, Ground state of scalar field equations involving a fractional Laplacian with general nonlinearity. Nonlinearity 26 (2013), no. 2, 479–494.

19.X. J. Chang, Multiplicity of solutions for semilinear elliptic problems with combined nonlinearities. Commun. Contemp. Math. 13 (2011), no. 3, 389–405.

20.X. J. Chang and Y. Li, Existence and multiplicity of nontrivial solutions for semilinear elliptic Dirichlet problems across resonance. Topol. Methods Nonlinear Anal. 36 (2010), no. 2, 285–310.

21. X. J. Chang, Y. Li and S. G. Ji, Nonresonance conditions on the potential with respect to the Fučík spectrum for semilinear Dirichlet problems. Z. Angew. Math. Phys. 61 (2010), no. 5, 823–833.

22. X. J. Chang and Q. D. Huang, Two-point boundary value problems for Duffing equations across resonance. J. Optim. Theory Appl. 140 (2009), no. 3, 419–430.