Daomin Cao, Professor of Mathematics,


Telephone: 010-62571859 

Address: 55 ZhongGuan Cun Dong Lu, Haidian District, Beijing, P.R.China

Postcode: 100190 

Research Areas

Partial Differential Equations, Nonlinear Analysis


-- Ph.D,  Academy of Mathematics and Systems Science, CAS, 1989

-- Master, Department of Mathematics, Xiangtan University, 1986

-- Bachelor, Department of Mathematics, Xiangtan University, 1983


[1] On the existence and nodal character of solutions of semilinear elliptic equations. Acta Mathematica Scientia, 8(1988),345-395.(with Zhu Xiping)
[2] The concentration-compactness principle in nonlinear elliptic equations. Acta Mathematica Scientia, 9(1989),307-323.(with Zhu Xiping)
[3] Bifurcation for quasilinear equations on $R^N$ with  natural growth conditions. Proc. Royal Soc. Edinburgh, 113A(1989), 215-228.(with  G.Li and S.Yan)
[4] Positive solutions and bifurcation from the essential spectrum of a semilinear elliptic equation on $R^N$. 
 Nonlinear Analysis,TMA, 15(1990), 1045-1052.
[5] Bifurcation for quasilinear elliptic system on $R^N$ with natural growth conditions. J. London Math.Soc., 44(1991),  514-524.
[6] Nontrivial solutions of semilinear elliptic equations with critical exponent in $R^2$. Comm. Part. Diff. Equat., 17(1992), 407-435.
[7] Multiple solutions of a Neumann problem in an exterior domain. Comm. Part. Diff. Equat., 18(1993), 687-700.
[8] Multiple solutions of a semilinear elliptic equation on $R^N$. Ann. Inst. H. Poincare, Anal. Non lineaire, 10(1993), 593-604.
[9] Multiple solutions of inhomogeneous elliptic equations involving critical Sobolev exponent. Proc. Royal Soc.Edinburgh, 124A(1994),  1177-1191.(with G.Li and H.Zhou)
[10] Multiple positive and nodal solutions for semilinear elliptic equations involving critical Sobolev exponents. Indiana Univ.Math. J., 44(1995), 1249-1271.(with E.S.Noussair)
[11] On the existence of multiple solutions of nonhomogeneous equations involving critical Sobolev exponent. Z. Angew. Math. Phys, 47(1996),  89-96.(with H.Zhou)
[12] Multiplicity of positive and nodal solutions for nonlinear elliptic problems. Ann. Inst.H. Poincare, Anal. Nonlineaire, 13(1996), 557-588.(with E.S.Noussair)
[13] On the existence and profile of multi-peaked solutions to singularly perturbed semilinear Dirichlet problems. Discrete and Continuous Dynamical System, 2(1996), 221-236.(with E.N.Dancer,
 E.S.Noussair and S.Yan)
[14] Existence and uniqueness results on single-peaked solutions of a semilinear problem. Ann. Inst. H.Poincare, Anal. Non lineaire, 15(1998), 73-111.(with E.S.Noussair and S.Yan)
[15] On the existence of multi-peaked solutions to a semilinear Neumann problem. Duke Math. J.,97(1999), 261-300. (with T.Kupper)
[16] Solutions with multiple "peaks" for nonlinear elliptic equations. Proc.Royal Soc.
Edinburgh,126A (1999), 235 - 264.(with E.S.Noussair and S.Yan)
[17] Multi-peak solutions for a singularly perturbed semilinear elliptic problem. J.Diff. Equat., 166 (2000), 266 -289.(with E.S.Noussair)
[18] Existence of symmetric multi- peaked solutions to singularly  perturbed semilinear problems. Comm. Part. Diff. Equat., 25(2000), 2185-2232.(with E.S.Noussair)
[19] Existence and nonexistence of interior-peaked solution for a nonlinear Neumann problem. Pacific J.Math.,200(2001), 19-40.(with E.S.Noussair and S.Yan)
[20] A Neumann problem in exterior domain, Manuscripta Mathematica.106(2001), 63-74.(with M. Lucia and H.S. Zhou)
[21] On the scalar curvature equation $-∆ u=(1+εK)u^{\frac{N+2}{N-2}}$ in $R^N$ . Calc. Var. and PDE, 15(2002), 403-419.(with E.S.Noussair and S.Yan)
[22] Uniqueness of positive multi-lump bound states of nonlinear Schrodinger equations. Math. Zeit., 243(2003), 599-642.(with H.P. Heinz)
[23] A compactness result for singular elliptic problems involving critical Sobolev exponent. Proc. Amer.Math. Soc.,131(2003), 1857 - 1866.(with S.Peng)
[24] Solutions for semilinear elliptic equations with critical exponents and Hardy potential. J. Diff. Equat., 205(2004), 521--537.(with P.Han)
[25] Multi-bump standing waves with a critical frequency for nonlinear Schrodinger equations. J. Diff. Equat., 203(2004), 292--312.(with E.S.Noussair)
[26] High energy positive solutions for Neumann problem for an elliptic system of equations with critical nonlinearity. Calc. Var. and PDE, 25(2005), 161-185. (with P. Han)
[27] Asymptotic behavior for elliptic problems with singular coefficient and nearly critical Sobolev growth. Annali di Mat. Pura ed Appl., 185 (2006), 189-205. (with S.Peng)
[28] Multi-bump bound states of Schrodinger equations with a critical frequency. Math. Ann., 336(2006), 925-948.(with S.Peng)
[29] Effective macroscopic dynamics of stochastic partial differential equations in perforated domains. SIAM J.Math.Anal., 38 (2007), 1508 -1527. (with J. Duan and W.Wang)
[30] Multiscale-bump standing waves with a critical frequency for nonlinear Schrodinger equations. Trans. Amer. Math. Soc.,360 (2008), 3813-3837.(with E.S.Noussair and S.Yan)
[31] Semi-classical bound states for Schrodinger equations with potentials vanishing or unbounded at infinity. Comm. Part. Diff. Equat., 34 (2009), 1566--1591.(with S.Peng)
[32] Infinitely many solutions for an elliptic problem involving critical Sobolev growth and Hardy potential. Calc. Var. and  PDE., 38(2010), 471-501.(with S.Yan)
[33] Multiplicity of solutions for the plasma problem in two dimensions. Adv. Math., 225 (2010), 2741-2785.(with S.Peng and S.Yan)
[34] Local exact controllability of the Navier-Stokes equations with the condition on the pressure on parts of the boundary. SIAM J. Control Optim., 48(2010), 3805-3837.(with T.Kim)
[35] Divergent solutions to the 5D Hartree equations. Colloq. Math., 125 (2011), 255-287.(with Q.Guo)
[36] Infinitely many solutions for p-Laplacian equation involving critical Sobolev growth. J. Funct. Anal., 262 (2012), 2861-2902.(with S.Peng and S.Yan)
[37] Continuous dependence of Cauchy problem for nonlinear Schrodinger equation in $H^s$. J. Diff. Equat., 255 (2013),2018-2064.(with W.Dai and W.Yang)
[38] Concentration of solutions for the Yamabe problem on half -spaces.  Proc. Roy. Soc. Edinburgh, Sect. A 143 (2013),no. 1, 73-99.(with S.Peng)
[39] On the Webster scalar curvature problem on the CR sphere with a cylindrical- type symmetry. J. Geom.  Anal., 23(2013),1674-1702. (with S.Peng and S.Yan)
[40] Minimal blow-up solutions of mass-critical inhomogeneous Hartree equation. J. Math. Phys.,
54 (2013), no. 12, 121511, 25 pp. (with Su Yiming)
[41] Regularization of point vortices pairs for the Euler equation in dimension two. Arch. Ration. Mech. Anal., 212 (2014), no. 1, 179–217. (with Liu Zhongyuan and Wei Juncheng)
[42] Uniqueness of positive bound states with multi-bump for nonlinear Schrödinger equations. Calc. Var. Partial Differential Equations, 54 (2015), no. 4, 4037–4063. (with  Li Shuanglong and Luo Peng)
[43] Dynamics for a stochastic reaction-diffusion equation with additive noise. J. Differential Equations, 259 (2015), no. 3, 838–872. (with Sun Chunyou and Yang Meihua)
[44] Planar vortex patch problem in incompressible steady flow. Adv. Math., 270 (2015), 263–301.
 (with  Peng Shuangjie and Yan Shusen)
[45] Non-stationary Navier-Stokes Equations with Mixed Boundary Conditions. J. Math. Sci. Univ. Tokyo, 24 (2017), 159–194.(with Tujin Kim)
[46] Nodal solutions for a supercritical semilinear problem with variable exponent. Calc. Var. Partial Differential Equations, 57 (2018), (with Li Shuanglong and Liu Zhongyuan)
[47]  Sign-changing bubble tower solutions for the supercritical Hénon-type equations. Ann. Mat. Pura. Appl. ,197(2018),1227–1246.(with Zhongyuan Liu and Shuangjie Peng)
[48] Nodal solutions for a supercritical semilinear problem with variable exponent. Calculus of Variations and Partial Differential Equations, 57(2018), Art. 38, 19 pp. (with Zhongyuan Liu and Shuanglong Li)
[49] Steady vortex patches with opposite rotation directions in a planar ideal fluid. Calculus of Variations and Partial Differential Equations, 58(2019) 58:75 (with Guodong Wang)
[50] Steady vortex patch solutions to the vortex-wave system. Nonlinearity,32(2019),1182-1904(with Guodong Wang)
[51] Nonlinear orbital stability for planar vortex patches. Proceedings of the American Mathematical Society,147(2019),775-784.(with Jie Wan and Guodong Wang)
[52] Classification of nonnegative solutions to a bi-harmonic equation with Hartree type nonlinearity.
Proceedings of the Royal Society of Edinburgh, 149(2019),979-994. (with Wei Dai)

[53] Local uniqueness for vortex patch problem in incompressible planar steady flow. Journal de Mathématiques Pures et Appliquées,131(2019), 251-289.(with Yuxia Guo, Shuangjie Peng and Shusen Yan)

[54] A note on steady vortex flows in two dimensions, Proceedings of the American Mathematical Society,148 (2020), 1153 -1159.with Guodong Wang

[55] Desingularization of vortices for 2D steady Euler flows via the vorticity method, SIAM J. Math., Anal. 522020),5363-5388 with G. Wang and W. Zhan

[56] Existence of Steady Multiple Vortex Patches to the Vortex-wave System, Pacific Math. J.,308(2020), 257-279. with Guodong Wang

[57] Steady vortex patch with polygonal symmetry for the planar Euler equations in a discNonlinear Analysis: Real World Applications, 51(2020), 103008 (with Jie Wan and Guodong Wang)

Research Interests

Partial Differential Equations of Elliptic Type,Equations Arising from Fluid, Calculus of Variations


已指导学生(Form Ph.D students advised by Daomin Cao)

彭双阶  博士研究生  070104-应用数学 (Shuangjie Peng)

 韩丕功  博士研究生  070104-应用数学 (Pigong      Han) 

 唐仲伟  博士研究生  070104-应用数学  (Zhongwei Tang)

杨卫华  博士研究生  070104-应用数学 (Weihua Tang)

王云鹏  硕士研究生  070104-应用数学  (Yunpeng Wang)

赵雷嘎  博士研究生  070104-应用数学  (Leiga  Zhao)

袁建军  博士研究生  070104-应用数学  (Jianjun Yuan)

张振辉  博士研究生  070104-应用数学 (Zhenghui Zhang) 

高善国  博士研究生  070104-应用数学  (Shanguo Gao)

郭青  博士研究生  070104-应用数学  (Qing Guo)

戴蔚  博士研究生  070104-应用数学  (Wei Dai)

刘忠原  博士研究生  070104-应用数学 (Zhongyuan Liu) 

吴丹  博士研究生  070104-应用数学  (Dan Wu)

苏一鸣  博士研究生  070104-应用数学  (YIming SU)

张杨  博士研究生  070104-应用数学  (Yang Zhang)

孙丕业  博士研究生  070104-应用数学  (Piye Sun)

李双龙  博士研究生  070104-应用数学  (Shuanglong Li)

李航  博士研究生  070104-应用数学  (Hang Li)

王国栋  博士研究生  070104-应用数学  (Guodong Wang)

万捷  博士研究生  070104-应用数学  (Jie Wan)

现指导学生(Ph.D students under advising of Daomin Cao)

詹伟城  博士研究生  070104-应用数学 (Weicheng Zhan)

邹昌君  博士研究生  070104-应用数学  (Changjun Zou)

秦国林  博士研究生  070104-应用数学 (Guolin Qin) 

余伟林  博士研究生  070104-应用数学  (Weilin Yu)

 赖善发  博士研究生  070104-应用数学  (Shanfa Lai)