
Professor Xingbin Pan 
• Professor of East China Normal University 
eMail: xbpan@math.ecnu.edu.cn
Phone Number(s):
Direct: +862162233519 +862154345089
Office:
Room A1501, Science Building, ZhongBei Campus Room 335, Math Building
Departmental Address:



Research Interests: 
Nonlinear partial differential equations and systems, calculus of variations, mathematical theory of superconductivity and liquid crystals. 
Recent Publications (from MathSciNet): 

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Selected Publications
Citations in the American Mathematical Society MathSciNet
Citations in the American Mathematical Society MathSciNet (access from outside of ECNU)：
http://www.ams.org/mathscinet/mrcit/individual.html?mrauthid=236649
[56] 

Meissner states of 3dimensional superconductors of type II, submitted. 
[55] 

On a linear differential operator involving Curl, submitted 
[54] 

Phase transition for potential with higher dimensional wells, submitted, (with Fanghua Lin and Changyou Wang) 
[53] 

Superconductivity near the normal state in a halfplane under the action of a perpendicular electric current and an induced magnetic field, Transactions of Amer. Math. Soc., to appear, (with Yaniv Almog and Bernard Helffer) 
[52] 

On a quasilinear system arising in the theory of superconductivity, Proc. Royal Soc. Edinburgh, vol. 141 A (2011), 397407, (with Gary Lieberman) 
[51] 

Asymptotics of solutions of a quasilinear system involving curl, J. Math. Phys., vol. 52 (2011), article no. 023517, 34pp. 
[50] 

Superconductivity near the normal state under the action of electric currents and induced magnetic fields in R^2, Comm. Math. Phys., vol. 300, no.1 (2010), 147184. (with Yaniv Almog and Bernard Helffer) 
[49] 

A Note on best Sobolev and relative isoperimetric constants and Neumann problems in exterior domains，《中国科技论文在线》，论文编号201002495（with Xuefeng Wang）. 
[48] 

Minimizing Curl in a multiconnected Domain, J. Math. Phys., vol. 50, no. 3, (2009), art. no. 033508. 
[47] 

On a quasilinear system involving the operator Curl, Calculus of Variations and PDE, vol. 36, no. 3 (2009), 317342. 
[46] 

An eigenvalue variation problem of magnetic Schrodinger operator in threedimensions, Disc. Contin. Dyn. Systems, special issue for Peter Bates’ 60th birthday, vol. 24, no. 3 (2009), 933978. 
[45] 

A threestage operatorsplitting/ finite element method for the numerical simulation of liquid crystal flow, International Journal of Numerical Analysis and Modeling, vol. 6, no. 3 (2009), 440454. (with R.Glowinski and P. Lin) 
[44] 

Nucleation of instability of Meissner state of superconductors and related mathematical problems, in: B. J. Bian, S. H. Li and X. J. Wang eds., Trends in Partial Differential Equations, for Prof Guangchang Dong’s 80th birthday, “Advanced Lectures in Mathematics”, ALM10, pp.323372, Higher Education Press and International Press, BeijingBoston, 2009. 
[43] 

Reduced Landaude Gennes functional and surface smectic state of liquid crystals, Journal of Functional Analysis, vol. 255, no. 11 (2008), 30083069. (with B. Helffer) 
[42] 

Critical elastic coefficient of liquid crystals and hysteresis, Comm. Math. Phys., vol. 280, no.1, (2008), 77121. 
[41] 

Nucleation of instability in Meissner state of 3dimensional superconductors, Comm. Math. Phys., vol. 276, no. 3, (2007), 571610. (with P. Bates) 
[40] 

Analogies between superconductors and liquid crystals: nucleation and critical fields, in: Asymptotic Analysis and Singularities, Advanced Studies in Pure Mathematics, Mathematical Society of Japan, Tokyo, vol.472 (2007); pp. 479517. 
[39] 

Nodal set of solutions of equations involving magnetic Schrodinger operator in three dimensions, J. Math. Phys., vol. 48, no. 5, (2007), article number 053521. 
[38] 

Magnetic fieldinduced instabilities in liquid crystals, SIAM J. Math. Anal., vol. 38, no. 5 (2007), 15881612, (with F. H. Lin) 
[37] 

Landaude Gennes model of liquid crystals with small GinzburgLandau parameter, SIAM J. Math. Anal., vol.37, no.5 (2006), 16161648. 
[36] 

Multiple states and hysteresis for type I superconductors, J. Math. Phys.,vol.46, no.7 (2005), Article no. 073301. (with Yihong Du). 
[35] 

Surface superconductivity in 3dimensions, Trans. Amer. Math. Soc., vol. 356 (10) (2004), 38993937. 
[34] 

Landaude Gennes model of liquid crystals and critical wave number, Comm. Math. Phys., vol. 239 (12) (2003), 343382. 
[33] 

Superconductivity near critical temperature, J. Math. Phys., vol. 44 (6) (2003), 26392678. 
[32] 

Superconducting films in perpendicular fields and effect of de Gennes parameter, SIAM J. Math. Anal., vol. 34 (4) (2003), 957991. 
[31] 

An operatorsplitting method for liquid crystal model, Comp. Phys. Comm., vol. 152 (3) (2003), 242252, (with R. Glowinski and P. Lin) 
[30] 

Upper critical field and location of surface nucleation of superconductivity, Ann. LHP Analyse Non Lineaire, vol. 20 (1), 2003, 145181. (with B. Helffer) 
[29] 

Surface superconductivity in applied magnetic fields above H_c2, Comm. Math. Phys., vol. 228 (2), (2002), 327370. 
[28] 

Upper critical field for superconductors with edges and corners, Calculus of Variations and PDE, vol. 14 (4) (2002), no. 4, 447482. 
[27] 

On a problem related to vortex nucleation of superconductivity, J. Differential Equations, vol. 182 (2002), 141168. (with K. H. Kwek) 
[26] 

Schrodinger operators with nondegenerately vanishing magnetic fields in bounded domains, Trans. Amer. Math. Soc., vol. 354 (10) (2002), 42014227. (with K. H. Kwek) 
[25] 

GinzburgLandau system and surface nucleation of superconductivity, Methods and Applications of Analysis, vol. 8 (2) (2001), 279300. (with K. Lu) 
[24] 

Surface nucleation of superconductivity in 3dimension, J. Differential Equations, vol. 168 (2) (2000), 386452. (with K. Lu) 
[23] 

Asymptotics of minimizers of variational problems involving curl functional, J. Math. Phys., vol. 41 (7) (2000), 50335063. (with Y. Qi) 
[22] 

Gauge invariant eigenvalue problems in R^2 and in R^2_+, Trans. Amer. Math. Soc., vol. 352 (3) (2000), 12471276. (with K. Lu) 
[21] 

Estimates of the upper critical field for the GinzburgLandau equations of superconductivity, Physica D, vol. 127 (12) (1999), 73104. (with K. Lu) 
[20] 

Eigenvalue problem of GinzburgLandau operator in bounded domains, J. Math. Phys., vol. 40 (6) (1999), 26472670. (with K. Lu) 
[19] 

Yamabe problem on half spaces, Nonlinear Anal. TMA, vol. 37 (2) (1999), 161186. (with G. Bianchi) 
[18] 

A variational problem of liquid crystals, Comm. in Applied Nonlinear Anal., vol. 5 (1) (1998), 131. (with Y. Yi) 
[17] 

Semilinear Neumann problem in an exterior domain, Nonlinear Anal. TMA, vol. 31 (7) (1998), 791821. (with X. Wang) 
[16] 

GinzburgLandau equation with De Gennes boundary conditions, J. Differential Equations, vol. 129 (1) (1996), 136165. (with K. Lu) 
[15] 

Least energy solutions of semilinear Neumann problems in R^4 and asymptotics, J. Math. Anal. Appl., vol. 201 (2) (1996), 532554. (with X. Xu) 
[14] 

Singular limit of quasilinear Neumann problems, Proc. Royal Soc. Edinburgh, vol. 125A (1) (1995), 205223. 
[13] 

Further study on the effect of boundary conditions, J. Differential Equations, vol. 117 (2) (1995), 446468. 
[12] 

Condensation of leastenergy solutions: The effect of boundary conditions, Nonlinear Anal. TMA, vol. 24 (2) (1995), 195222. 
[11] 

Condensation of leastenergy solutions of a semilinear Neumann problem, J. Partial Differential Equations, vol. 8 (1) (1995), 136. 
[10] 

The Melnikov method and elliptic equations with critical exponent, Indiana Univ. Math. J., vol. 43 (3) (1994), 10451077. (with R. Johnson and Y. Yi) 
[9] 

Singular solutions of the elliptic equation Delta uu+u^p=0, Ann. Mat. Pura Appl., vol. 166 (4) (1994), 203225. (with R. Johnson and Y. Yi) 
[8] 

Positive solutions of supercritical elliptic equations and asymptotics, Comm. Partial Differential Equations, vol. 18 (56) (1993), 9771019. (with R. Johnson and Y. Yi) 
[7] 

Singular ground states of semilinear elliptic equations via invariant manifold theory, Nonlinear Anal. TMA, vol. 20 (11) (1993), 12791302. (with R. Johnson and Y. Yi) 
[6] 

On an elliptic equation related to the blowup problem of the nonlinear Schrodinger equation, Proc. Royal Soc. Edinburgh, vol. 123A (4) (1993), 763782. (with R. Johnson) 
[5] 

Positive solutions of the elliptic equation Delta u+u^{(n+2)/(n2)}+K(x)u^q=0 in R^n and in balls, J. Math. Anal. Appl., vol. 172 (2) (1993), 323338. 
[4] 

Blowup behavior of ground states of semilinear elliptic equations in R^n involving critical Sobolev exponents, J. Differential Equations, vol. 99 (1) (1992), 78107. (with X. Wang) 
[3] 

Singular behavior of leastenergy solutions of a semilinear Neumann problem involving critical Sobolev exponents, Duke Math. J., vol. 67 (1) (1992), 120. (with W. M. Ni and I. Takagi) 
[2] 

Positive solutions of Delta u+K(x)u^p=0 without decay conditions on K(x), Proc. Amer. Math. Soc., Vol. 115 (3) (1992), 699710. 
[1] 

Existence of singular solutions of a semilinear elliptic equation in R^n, J. Differential Equations, vol. 94 (1) (1991), 191203. 

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