PERSONAL INFORMATION
Name: Shuangjie PENG, Professor
Address: School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China
E-mail:sjpeng@mail.ccnu.edu.cn
Phone: 86-27-67862057
EDUCATION
Ph.D. Mathematics,Academy of Mathematical and System Sciences, Chinease Academy of Sciences, 2003. Dissertation: On Semilinear Elliptic Equations. Advisor: Professor Daomin Cao.
M.A.Mathematics, Central China Normal University, 1998.
B.A.Mathematics, Hubei University, 1990.
RESEARCH INTERESTS AND CURRENT RESEARCH WORKS
Nonlinear Functional Analysis; Nonlinear Elliptic Equations; Singularly Perturbed Problems
We are interested in the theory on nonlinear functional analysis and its application to nonlinear partial differential equations. The main fields focus on semilinear elliptic equations, nonlinear Schrodinger equations (systems), free boundary problems. We worked there mainly to find concentration solutions to these problems. For examples, we constructed semiclassical bumped solutions concentrating on highter dimensional manifolds to these types of problems, we also studied a type of Schrodinger equations with compact supported potentials and obtained multiple semi-classical solutions. Currently, we are focusing on nonlinear Schrodinger systems and p-Laplacian problems, we intend to find some solutions with some prescribed properties.
MAIN ACADEMIC VISITS
2004, 01--2005, 07: A Humboldt Fellow in Mathematisches Institut,
Universit\"{a}t Giessen, Germany
2006, 05--2006, 07: Academy of Mathematics and System Sciences,
Chinese Academy of Sciences
2007, 06--2007, 08: Academy of Mathematics and System Sciences,
Chinese Academy of Sciences
2007, 10--2007, 11: School of Mathematics, Statistics and Computer Science,
The University of New England, Australia
2009, 01--2009, 05: Department of Mathematics, The University of Iowa, USA
2010, 10--2010, 11: School of Mathematics, Statistics and Computer Science,
The University of New England, Australia
2011, 03--2011, 03: Department of Mathematics, The University of Iowa, USA
2011, 12--2011, 12: Chern Institute of Mathematics, Nankai University, P. R. China
2012, 04--2012, 06: School of Mathematics, Statistics and Computer Science,
The University of New England, Australia
2012, 10--2012, 11: Taida Institute of Mathematical Sciences,
National Taiwan University, Taiwan
2012, 12--2012, 12: Center for Partial Differential Equations, East China Normal
University, P. R. China
2013, 07--2013, 08: Department of Mathematics, The Wright State University, USA
2014, 01--2014, 02: Institute of Mathematical Science,
Chinese University of HongKong, HongKong
2014, 06--2014, 07: Taida Institute of Mathematical Sciences,
National Taiwan University, Taiwan
2014, 09--2014, 10: School of Mathematics, Statistics and Computer Science,
The University of New England, Australia
2014, 11--2014, 11: Institute of Mathematical Science,
Chinese University of HongKong, HongKong
2014, 12--2014, 12: Institute of Mathematical Science,
National University of Singapore, Singapore
INVITED SEMINARS
2004, 06--2004, 07: ETH Lausanna, Switzerland
2004, 07--2004, 07: Universit\"{a}t Z\"{u}rich, Switzerland
2004, 11--2004, 11: Mathematisches Institut, Universit\"{a}t Cottbus, Germany
2005, 06--2005, 06: Universit\"{a}t Mainz, Germany
2005, 06--2005, 07: Oberwolfach Mathematisches Institut, Germany
2007, 10--2007, 10: The University of New England, Australia
2009, 01--2009, 05: The University of Iowa, USA
2010, 10--2010, 11: The University of New England, Australia
2011, 03--2011, 03: The University of Iowa, USA
2011, 03--2011, 03: The Institute of Illinois, USA
2012, 04--2012, 04: The University of New South Wales, Australia
2012, 11--2012, 11: CIRM Luminy, France
2013, 07--2013, 07: ICCM, National Taiwan University, Taiwan
2013, 09--2013, 07: Nankai University, China
2014, 01--2014, 02: Chinese University of HongKong, HongKong
2014, 09--2014, 10: The University of New England, Australia
2014, 11--2014, 11: Chinese University of HongKong, HongKong
2014, 12--2014, 12: National University of Singapore, Singapore
FOUNDATIONS
1. Program for Changjiang Scholars and Innovative Research Team in University
(Grant No. IRT13066): On Nonlinear Partial Equations, 2014,01-2016,12.
2. Funds of Distinguished Young Scholar from NSFC (Grant No. 11125101): On
nonlinear functional analysis, 2012,01-2015,12.
3. The Key Project of Hubei Province for Cultivating High Level Talents, 2012,01
-2016,12.
4. PHD specialized grant of the Ministry of Educations of China (Grant No.
20110144110001): Study on some typical problems of elliptic pequations,
2012,01-2014,12.
5. The National Natural Science Foundation of China (Grant No.11071092):
Some typical problems on the study of nonlinear Schr\"{o}dinger equations and
free boundary problems,2011,01-2013,12.
6. The National Natural Science Foundation of China (Grant No.10571089):
Nonlinear Elliptic and Obstacle Problem, 2006,01-2008,12.
7. The National Natural Science Foundation of China (Grant No.10631030): On
the Theory of Nonlinear Elliptic and Parabolic Equations, 2007,01-2010,12.
8. Program for New Century Excellent Talents in University (Grant No. 07-0350),
2008,01-2010,12.
9. The Key Project of Chinese Ministry of Education (Grant No. 107081): On
the Schr\"{o}dinger Equation with Electromagnetic Fields, 2007,01-2009,12.
10. The Scientific Research Foundation for the Returned Overseas Chinese
Scholars,State Education Ministry: On the singularly Perturbed Elliptic
Equations, 2007,01-2007,12.
PUBLICATIONS
64. Wei Long and Shuangjie Peng: Multiple positive solutions for a type of nonlinear Schrodinger
equations, Ann. Sc. Norm. Super. Pisa, Cl. Sci., to appear.
63. Shuangjie Peng and Huirong Pi: Spike vector solutions for some coupled nonlinear Schrodinger
equations, Discrete Contin. Dyn. Syst., to appear.
62. Shuanjie Peng and Jing Yang: Multiple positive solutions for a nonlinear elliptic equation
involving Hardy-Sobolev-Maz’ya term, Acta Math. Sinica, to appear.
61. Wei Long, Shuanjie Peng and Jing Yang: Infinitely many positive solutions and sign-changing
solutions for nonlinear fractional Schrodinger equations, Discrete Contin. Dyn. Syst.,
to appear.
60. Daomin Cao, Shuangjie Peng and Shusen Yan: Planar vortex patch problem in incompressible steady
flow, Adv. Math., 270(2015), 263-301.
59. Yi Li and Shuangjie Peng: Multi-peak solutions to two types of free boundary problems, Calc. Var.
Partial Differential Equations, in press.
58. Yinbin Deng, Shuangjie Peng and Shusen Yan: Positive soliton solutions for generalized quasilinear
Schrodinger equations with critical growth, J. Differential Equations, 258(2015), 115-147.
57. Shuangjie Peng and Chunhua Wang: Infinitely many solutions for a Hardy-Sobolev equation involving
critical growth.Math. Methods Appl. Sci., 38(2015),197–220
56.Yinbin Deng, Shuangjie Peng and Jixiu Wang: Nodal soliton solutions for generalized quasilinear
Schrodinger equations, J. Math. Phys., 55(2014), 051501，16pp
55.Shuangjie Peng and Huirong Pi: Boundary concentrating solutions for a Henon-like equation,
Proc. Roy. Soc. Edinburgh Sect. A, to appear
54. Wei Long and Shuangjie Peng: segregated vector solutions for a class of Bose-Einstein systems,
J. Differential Equations, 257(2014),207-230.
53. Chang-Shou Lin and Shuangjie Peng: Segregated vector solutions for linearly coupled nonlinear
Schrodinger systems, Indiana Univ. Math. J., 63(2014), 939-967.
52. Yi He, Gongbao Li and Shuangjie Peng: Concentrating bound states for Kirchhoff type problems
in R^3 involving critical Sobolev exponents, Adv. Nonlin.Studies, 14(2014), 441-468.
51. Yinbin Deng, Shuangjie Peng and Huirong Pi: Bound states with clustered peaks for nonlinear
Schrodinger equations with compactly supported potentials, Adv. Nonlin.Studies, 14(2014), 421-439.
50. Shuangjie Peng and Yanfang Peng: Least energy sign-changing solutions for a singular elliptic
equation in lower dimensions, Comm. Contem. Math., 16(2014), no.4, 1350048, 16pp
49. Yinbin Deng, Shuangjie Peng and Li Wang: Infinitely many radial solutions to elliptic system involving
critical exponents, Discrete Contin. Dyn. Syst., 34(2014), 461-475.
48. Daomin Cao, Shuangjie Peng and Shusen Yan: On the Webster scalar curvature problem on the CR
sphere with a cylindrical-type symmetry, J. Geom. Anal., 23(2013), 1674-1702.
47. Yinbin Deng, Shuangjie Peng and Jixiu Wang: Nodal soliton solutions for quasilinear Schrodinger
equations with critical exponent, J. Math. Phys. 54(2013), no.1, 011504, 28pp.
46. Shuangjie Peng and Zhi-Qiang Wang: Segregated and synchronized vector solutions for nonlinear
Schrodinger systems, Arch. Ration. Mech. Anal., 208(2013), 305-339.
45. Daomin Cao and Shuangjie Peng:Concentration of solutions for the Yamabe problem on half-spaces,
Proc. Roy. Soc. Edinburgh Sect. A, 143(2013), 73-99.
44. Dongsheng Kang and Shuangjie Peng: Infinitely many solutions to elliptic systems with critical
exponents and Hardy potentials, Sci. China Math, 55 No.10 (2012)，2027-2044.
43. Yinbin Deng, Lingyu Jin and Shuangjie Peng: Solutions of Schrodinger equations with inverse
square potential and critical nonlinearity, J. Differential Equations, 253(2012), 1376-1398.
42. Daomin Cao, Shuangjie Peng and Shusen Yan: Infinitely many solutions for p-Laplacian equation
involving critical Sobolev growth, J. Funct. Anal., 262(2012), 2861-2902.
41. Yinbin Deng, Shuangjie Peng and Li Wang: Existence of multiple solutions for a nonhomogeneous
semilinear elliptic equation involving critical exponent, Discrete Contin. Dyn. Syst., 32(2012),
795-826.
40.Gongbao Li, Shuangjie Peng and Chunhua Wang: Infinitely many solutions for nonlinear Schr\"{o}dinger
equations with electromagnetic fields, J. Differential Equations, 251(2011), 3500-3521.
39. Gongbao Li, Shuangjie Peng and Chunhua Wang: Multi-bump solutions for the nonlinear
Schr\"{o}dinger-Poisson system, J. Math. Phys. 52(2011), no.5, 053505, 19 pp.
38. Yinbing Deng, Shuangjie Peng and Jixiu wang: Infinitely many sign-changing solutions for
quasilinear Schrodinger equations in R^N, Commun.Math.Sci. 9(2011), 859-878.
37.Dongsheng Kang and Shuangjie Peng: Existence and asymptotic properties of solutions to elliptic
systems involving multiple critical exponents, Sci.China Math, 54(2011), 243-256.
36. Yi Li and Shuangjie Peng: Multiple solutions for an elliptic problem related to vortex pairs,
J. Differential Equations, 250(2011), 3448-3472.
35. Daomin Cao, Shuangjie Peng and Shusen Yan: Multiplicity of solutions for the plasma problem
in two dimensions, Adv. Math., 225(2010), 2741-2785.
34. Na Ba, Yinbin Deng and Shuangjie Peng: Multi-peak bound states for Schrodinger equations
with compactly supported or unbounded potentials, Ann. Inst. H. Poincaré Anal. Non Linéaire
27(2010), 1205-1226.
33. Thomas Bartsch and Shuangjie Peng:Solutions concentrating on higher dimensional subsets
for singularly perturbed elliptic equations II, J. Differential Equations, 248(2010), 2746-2767.
32. Gongbao Li, Shuangjie Peng and Shusen Yan: Infinitely many positive solutions for the nonlinear
Schrodinger-Poisson system, Comm. Contem. Math., 12(2010), 1069-1092..
31. Shuangjie Peng and Jing Zhou, Concentration of solutions for a Paneitz type problem,
Discrete Contin. Dyn. Syst., 26（2010）1055-1072.
30. Daomin Cao and Shuangjie Peng, Semi-classical bound states for Schrodinger equations with
potentials vanishing or unbounded at infinity, Comm. Partial Differential Equations,
34(2009),1566-1591.
29. Bingyu Kou and Shuangjie Peng, Quasilinear elliptic equations with Neumann boundary and
singularity, Acta Math. Appl. Sin., 25 (2009),
28. Shujuan Li and Shuangjie Peng, Asymptotic behavior on the Henon equation with supercritical
exponent, Sci. China, 52(2009), 2185-2194.
27. Daomin Cao, Shuangjie Peng and Shusen Yan, Asymptotic behavior of ground state solutions for
the Henon equation, IMA J. Appl. Math.,74(2009), 468-480.
26. Daomin Cao and Shuangjie Peng, Solutions for the prescribing mean curvature equation,
Acta Math. Appl. Sin., 24(2008),497-510.
25. Yinbin Deng, Lingyu Jin and Shuangjie Peng: Positive solutions for elliptic equations related to
the Caffarelli-Kohn-Nirenberg inequalities, Comm. Contem. Math., 11(2009), 185-199.
24.Thomas Bartsch and Shuangjie Peng : Solutions concentrating on higher dimensional subsets
for singularly perturbed elliptic equations I, Indiana Univ.Math. J. 57(2008),1599-1632.
23.Gongbao Li and Shuangjie Peng: Remarks on elliptic problems involving the Caffarelli-Kohn-
Nirenberg inequalities, Proc. Amer. Math. Soc.. 136(2008),1221-1228.
22.Thomas Bartsch, Shuangjie Peng and Zhitao Zhang: Existence and non-existence of solutions
to ellipticm equations related to the Caffarelli-Kohn-Nirenberg inequalities,
Calc. Var. Partial Differential Equations 30 (2007),113-136.
21. Yinbin Deng, Lingyu Jin and Shuangjie Peng: A Robin boundary problem with Hardy potential and
critical nonlinearities, Journal d'Analyse Mathematique, 104(2008), 125-154.
20.Gongbao Li, Shuangjie Peng and Shusen Yan: A new type of solutions for a singularly perturbed
elliptic Neumann problem, Revista Mat. Iberoa.,23(2007),1039-1066.
19.Dongsheng Kang and Shuangjie Peng: Singular elliptic problems in with critical Sobolev–Hardy
exponents, Nonlin. Analysis, TMA, 68(2008), 1332-1345.
18. Thomas Bartsch and Shuangjie Peng: Semiclassical symmetric Schrodinger equations:
existence of solutions concentrating simultaneously on several spheres, Zeit. Angew. Math. Phys.,
58(2007), 778-804.
17. Daomin Cao and Shuangjie Peng: Multi-bump bound states of Schrodinger equations with a
critical frequency, Math. Ann., 336(2006):925-948.
16.Thomas Bartsch, E.Norman Dancer and Shuangjie Peng: On multibump semi-classical bound states of
nonlinear Schrodinger equations with electromagnetic fields, Adv. Diff. Equations, 7 (2006), 781-812.
15. Wenliang Gao and Shuangjie Peng, An elliptic equation with combined critical Sobolev-Hardy terms,
Nonlinear Analysis, TMA,65(2006), 1595-1612.
14. Daomin Cao and Shuangjie Peng: Asymptotic behavior for elliptic problems with singular coefficient
and nearly critical Sobolev growth, Annali di Mathematica Pura ed Applicata, 185(2006), 189-205.
13. Shuangjie Peng: Multiple boundary concentrating solutions to Dirichlet problem of Henon equation,
Acta Mathematicate Applicate Sinica, 22(2006), 137-162.
12. Shuangjie Peng: Remarks on singular critical growth elliptic equation, Discrete Contin.
Dyn. Syst., 14(2006),707-719.
11. Daomin Cao, Xiaoming He and Shuangjie Peng: Positive solutions for some singular critical growth
nonlinear elliptic equations,Nonlinear Analysis TMA, 60(2005), 589-609.
10. Dongsheng Kang and Shuangjie Peng: Solutions for semilinear elliptic problems with critical
Sobolev-Hardy exponents and Hardy potential, Applied Math. Letter, 18(2005), 1094-1100.
9. Dongsheng Kang and Shuangjie Peng: Multiple solutions for elliptic problems with critical
Sobolev-Hardy exponents. Israel Mathematical Journal, 143(2004), 281-297.
8. Dongsheng Kang and Shuangjie Peng: Existence of solutions for elliptic equations with critical
Sobolev-Hardy exponents, Nonlinear Analysis TMA., 56 (2004), 1151--1164.
7. Dongsheng Kang and Shuangjie Peng: Sign-changing solutions for elliptic problems with critical
Sobolev-Hardy exponents. Jour. Math. Anal. Appl., 291 (2004), 488—499.
6. Shuangjie Peng: Uniqueness of the symmetric single peak solutions to Neumann problem with
critical Sobolev exponent, Nonlinear Analysis, TMA., 56(2004),19-42.
5. Dongsheng Kang and Shuangjie Peng: Positive solutions of singular elliptic equations,
Applied Math.Letter, 17(2004), 411-416.
4. Daomin Cao and Shuangjie Peng: A note on the sign-changing solutions to elliptic problems
with critical Sobolev exponent and Hardy terms, J. Differential Equations, 193(2003), 424-434.
3. Daomin Cao and Shuangjie Peng: A global compactness result for singular elliptic problems
involving critical Sobolev exponent, Proc.Amer.Math.Soc., 131(2003), 1857-1866.
2. Daomin Cao and Shuangjie Peng: The asymptotic behavior of the ground state solutions for
Henon equation, Jour. Math. Anal. Appl.,278(2003), 1-17
1.Yinbin Deng and Shuangjie Peng: Existence of multiple positive solutions for inhomogeneous
Neumann problem, Jour. Math. Anal. Appl.,271(2002). 155-174.
