代丽美，教授，潍坊市专业技术拔尖人才，潍坊市优秀科技工作者。主要从事偏微分方程理论及其应用的研究。

招生专业：电子信息

研究方向：偏微分方程理论及其应用

联系方式：limeidai@126.com

学术成果：

1.Limei Dai, Jiguang Bao and Bo Wang. Solvability of Hessian quotient equations in exterior domains. Canadian Journal of Mathematics. 2025;77(1):118-148.

2.Limei Dai and Xuewen Guo. Parabolic Hessian equations outside a bowl-shaped domain, Communications on Pure and Applied Analysis Vol. 23, No. 1 (2024) , pp. 112-130.

3.Limei Dai, The Solutions with Prescribed Asymptotic Behavior for the Exterior Dirichlet Problem of Hessian Equations, Analysis in Theory and Applications, Vol. 39, No. 2 (2023), pp. 120-146.

4.Limei Dai, Jiguang Bao. Entire Solutions of Cauchy Problem for Parabolic Monge-Ampere Equations. Advanced Nonlinear Studies 20 (2020), no. 4, 769--781.

5.Yuebin Hao, Limei Dai. Symmetry results for viscosity solutions of fully nonlinear equations in annular and exterior domains, Journal of Mathematical Analysis and Applications, Volume 485, Issue 1, 2020, 123776 

6.Limei Dai. Existence and nonexistence of subsolutions for augmented Hessian equations, Discrete and Continuous Dynamical Systems, Volume 40, Number 1, January 2020 pp. 579-596.

7.Limei Dai and Hongyu Li. Entire subsolutions of Monge-Ampère type equations. Communications on Pure & Applied Analysis, 2020, 19(1): 19-30.

8.代丽美. 抛物型Hessian方程的外问题. 数学进展, 45(4) (2016), 561-571.

9.Limei Dai. Symmetry of viscosity solutions for fully nonlinear parabolic equations. Nonlinear Analysis: Real World Applications, 29 (2016), 68-79.

10.Limei Dai.  Exterior problems for more general parabolic Monge–Ampère equation in more general domain. Journal of Mathematical Analysis and Applications, 427 (2015), 1190–1204.

11.代丽美. 外区域上的抛物型Monge-Ampere方程. 数学学报，58(3) 2015, 447-456.

12.Limei Dai. Exterior problems of parabolic Monge-Ampere equations for n=2. Computers & Mathematics with Applications, 67 (2014), 1497-1506.

13.Limei Dai. Exterior problems for a parabolic Monge-Ampere equation. Nonlinear Analysis: Theory, Methods & Applications, 100(2014), 99-110.

14.Limei Dai. Multi-valued solutions to a class of parabolic Monge-Ampère equations. Communications on Pure and Applied Analysis, 13(2014), 1061-1074.

15.Haigang Li, Limei Dai. The exterior Dirichlet problem for Hessian quotient equations. Journal of Mathematical Analysis and Applications, 393(2) (2012), 534-543.

16.代丽美，秦国红. Hessian商方程具有渐近性质的整体解. 数学物理学报，2012, 32A (3): 566–575.

17.Limei Dai, Jiguang Bao. Multi-valued solutions to fully nonlinear uniformly elliptic equations. Journal of Mathematical Analysis and Applications, 389(1), (2012) 314-321.

18.Limei Dai, Multi-valued solutions to Hessian quotient equations. Communications in Mathematical Sciences, 10(2) (2012), 717-733.

19.代丽美. 完全非线性一致椭圆方程的外问题. 数学年刊, 32A(6) 2011, 721-728.

20.Limei Dai, Entire solutions with asymptotic behavior of fully nonlinear uniformly elliptic equations, Communications on Pure and Applied Analysis, 10(6) (2011), 1707-1714.  

21.Limei Dai, Jiguang Bao, Multi-valued solutions to Hessian equations, Nonlinear Differential Equations and Applications, 18 (2011), 447-457.

22.Limei Dai, Existence of solutions with asymptotic behavior of exterior problems of Hessian equations, Proceedings of the American Mathematical Society, 139 (8) (2011), 2853-2861.

23.Limei Dai, The Dirichlet problem for Hessian quotient equations in exterior domains, Journal of Mathematical Analysis and Applications, 380 (2011), 87–93.

24.Limei Dai, Existence of multi-valued solutions with asymptotic behavior of Hessian equations, Nonlinear Analysis, 74 (2011), 3261-3268.

25.Limei Dai and Jiguang Bao, On uniqueness and existence of viscosity solutions to Hessian equations in exterior domains, Frontiers of Mathematics in China, 6(2) (2011), 221--230.  

26.Limei Dai, Multiple solutions to Hessian equations, Manuscripta Mathematica, 134 (2011), 423--433.

27.Limei Dai and Hongyu Li.Positive solutions of singular Emden-Fowler boundary value problem with negative exponent and multiple impulses.Nonlinear  Analysis,2009,70(10):3682-3695.

科研项目及获奖：

[1]2013.01.01-2015.12.31，抛物型Monge-Ampere方程的外问题与多值解(11201343)，国家自然科学基金青年科学基金项目，主持

[2]2011.07-2014.07，具有奇性的Hessian型方程，山东省优秀中青年科学家科研奖励基金(BS2011SF025)，主持

[3]2018.04-2020.08，Monge-Ampere型方程几个问题的研究，山东省自然科学基金(ZR2018LA006)，主持

[4]2022.01-2024.12，抛物型Monge-Ampere方程解的渐近行为研究,山东省自然科学基金(ZR2021MA054)，主持

[5]2012.01-2013.12，Monge-Ampère方程与最优运输问题，山东省科技发展计划(2011YD16002)，主持.

[6]2012.12，山东省高等学校优秀科研成果三等奖，二阶椭圆型方程的若干问题，1/1

[7]2014.06，山东省优秀学位论文指导教师

[8]2017.04，第九届潍坊市青年科技奖

[9]2015.09，潍坊市自然科学二等奖，非线性椭圆与抛物方程的一些进展，1/1

[10]2014.10，潍坊市自然科学三等奖，非线性偏微分方程解的存在性及对称性，1/1