基本情况

张学梅，理学博士，华北电力大学数理学院教授，硕士生导师。2001年7月于山东大学数学学院获得理学硕士学位，2010年7月于北京理工大学数学与统计学院获得理学博士学位。博士学位论文荣获北京理工大学2011年度优秀博士学位论文。2015年9月-2016年9月及2023年9月-2024年9月在澳大利亚新英格兰大学做访问学者，合作导师：杜一宏院士。荣获2008年度和2009年度华北电力大学科技工作先进个人。2013年7月荣获第九届全国微分方程稳定性暨全国金融数学学术会议优秀论文奖。现担任《理论数学》杂志编委。

研究领域

非线性泛函分析、非线性微分方程及其应用

科研项目

主持国家自然科学基金面上项目一项，主持国家自然科学基金青年基金项目一项，主持北京市自然科学基金面上项目一项，参与北京市自然科学基金项目两项，主持中央高校基本科研业务费项目2项。

1. 国家自然科学基金面上项目，Monge-Ampère方程和k-Hessian方程解的存在性与边界渐近行为研究，主持，2024-2027.

2. 国家自然科学基金青年基金项目，广义平均曲率方程中的非线性分析研究，主持，2014-2016.

3.北京市自然科学基金面上项目，k-Hessian方程Dirichlet和边界爆破问题解的研究，主持，2023-2025.

4.北京市自然科学基金面上项目，k-Hessian方程和方程组的可解性研究，参加，2021-2023.

5.北京市自然科学基金预探索项目，相对论算子方程正解的精确个数及其分岔研究，参加，2016-2017.

6.中央高校基本科研业务费项目，Banach空间中分数阶微分方程及其应用，主持，2014-2015.

7.中央高校基本科研业务费项目，非线性脉冲微分系统及其应用研究，主持，2011-2013.

论文发表

共发表论文60余篇，被SCI收录50余篇，其中ESI高被引论文4篇。出版专著一部。

1. 冯美强,张学梅.Monge-Ampère方程边界爆破解的最优估计和不存在性[J].数学物理学报（A辑）,2023,43(01):181-202.

2. Feng, Meiqiang,Zhang, Xuemei.Strictly Convex Solutions to the Singular Boundary Blow-Up Monge-Ampère Problems: Existence and Asymptotic Behavior[J].JOURNAL OF GEOMETRIC ANALYSIS,2024,34(10).DOI:10.1007/s12220-024-01753-z.

3. Zhang, Xuemei,Yang, Yuyao.Necessary and sufficient conditions for the existence of entire subsolutions to p-k-Hessian equations[J].NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,2023,233.DOI:10.1016/j.na.2023.113299.

4. Zhang, Xuemei,Feng, Meiqiang.Boundary blow-up solutions to singular k-Hessian equations with gradient terms: Sufficient and necessary conditions and asymptotic behavior[J].JOURNAL OF DIFFERENTIAL EQUATIONS,2023,375:475-513.DOI:10.1016/j.jde.2023.08.022.

5. 张学梅,阚士坤.SUFFICIENT AND NECESSARY CONDITIONS ON THE EXISTENCE AND ESTIMATES OF BOUNDARY BLOW-UP SOLUTIONS FOR SINGULAR p-LAPLACIAN EQUATIONS[J].Acta Mathematica Scientia,2023,43(03):1175-1194.DOI:10.1007/s10473-023-0311-4.

6. Zhang, Xuemei,Kan, Shikun.Sufficient and Necessary Conditions on the Existence and Estimates of Boundary Blow-Up Solutions for Singular p-Laplacian Equations[J].ACTA MATHEMATICA SCIENTIA,2023,43(03):1175-1194.DOI:10.1007/s10473-023-0311-4.

7. Zhang, Xuemei,Bai, Shuangshuang.Existence and boundary asymptotic behavior of strictly convex solutions for singular Monge-Amp?re problems with gradient terms[J].PORTUGALIAE MATHEMATICA,2023,80(1-2):107-132.DOI:10.4171/PM/2097.

8. Kan, Shikun,Zhang, Xuemei.Entire positive p-k-convex radial solutions to p-k-Hessian equations and systems[J].LETTERS IN MATHEMATICAL PHYSICS,2023,113(01).DOI:10.1007/s11005-023-01642-6.

9. Feng, Meiqiang,Zhang, Xuemei.The existence of infinitely many boundary blow-up solutions to the p-k-Hessian equation[J].ADVANCED NONLINEAR STUDIES,2023,23(01).DOI:10.1515/ans-2022-0074.

10. Yang, Yuyao,Zhang, Xuemei.Necessary and sufficient conditions of entire subsolutions to Monge-Ampere type equations[J].ANNALS OF FUNCTIONAL ANALYSIS,2023,14(01).DOI:10.1007/s43034-022-00228-y.

11. Feng, Meiqiang,Zhang, Xuemei.Nontrivial Solutions for the Polyharmonic Problem: Existence, Multiplicity and Uniqueness[J].FRONTIERS OF MATHEMATICS,2023,18(02):307-340.DOI:10.1007/s11464-021-0190-8.

12. X. Zhang, M. Feng, Blow-up solutions to the Monge-Ampère equation with a gradient term: sharp conditions for the existence and asymptotic estimates. Calc. Var. Partial Differential Equations, 61 (2022) 208.

13. X. Zhang, Y. Du. Sharp conditions for the existence of boundary blow-up solutions to the Monge-Ampère equation. Calc. Var.Partial Differential Equations, 57（2018）30.

14. X. Zhang, M. Feng, Boundary blow-up solutions to singular k-Hessian equations with gradient terms: Sufficient and necessary conditions and asymptotic behavior. J. Differential Equations 375 (2023) 475-513.

15. X. Zhang, M. Feng, The existence and asymptotic behavior of boundary blow-up solutions to the k-Hessian equation, J. Differential Equations 267 (2019) 4626-4672.

16. X. Zhang, Y. Yang, Necessary and sufficient conditions for the existence of entire subsolutions to p-k-Hessian equations. Nonlinear Anal. 233 (2023) 113299

17. X. Zhang, M. Feng, Boundary blow-up solutions to the k-Hessian equation with singular weights. Nonlinear Anal. 167 (2018) 51-66.

18. X. Zhang, M. Feng, Bifurcation diagrams and exact multiplicity of positive solutions of one-dimensional prescribed mean curvature equation in Minkowski space. Commun. Contemp. Math. 21 (2019) 1850003.

19. X. Zhang, M. Feng, Boundary blow-up solutions to the Monge-Ampère equation: Sharp conditions and asymptotic behavior, Adv. Nonlinear Anal. 9（2020）729-744.

20. X. Zhang, M. Feng, Double bifurcation diagrams and four positive solutions of nonlinear boundary value problems. Commun. Pur. Appl. Anal. 17 (2018) 2149-2171.

21. 张学梅，冯美强，非线性微分方程的可解性理论及其应用。北京，科学出版社，2015。