Publications and Presentations by Junping Shi

Presentations:

  1. Optimal Spatial Harvesting Strategy and Symmetry-Breaking (pdf) June 2006
  2. Bistable dynamics in autocatalytic chemical reactions (pdf) June 2006
  3. Bistability in chemical reactions and predator-prey systems (pdf) March 2006
  4. A variational problem in climate dynamics (powerpoint) April 2005
  5. Allee Effect and Bistability in Spatially Heterogeneous Predator-Prey Models (pdf) April 2005
  6. Isothemal Balls in an autocatalytic chemical reaction (pdf) Feb 2005
  7. Bistability, Allee Effect and Threshold Manifold in Structured Population Models (powerpoint) Jan 2005
  8. Pattern formations in Mathematical Biology (undergraduate lecture, partly in Chinese) (Powerpoint) May 2004
  9. Reaction-diffusion models with Allee effect (Powerpoint) May 2004
  10. Asymptotic Spatial Patterns and Entire Solutions (pdf) June 2003

Papers (in refereed journal): (pdf files)


1. Exact multiplicity of positive solutions for a class of semilinear problem (with Tiancheng Ouyang)
    (Journal of Differential Equations, Volume 146, No. 1, pg. 121--156, 1998)

2.  On a Singular Nonlinear Semilinear Elliptic Problem (with Miaoxin Yao)
     (Proceedings of Royal Society of Edinburgh, Series A, Vol. 128, No. 6, pg. 1389-1401, 1998)

3.   Multi-spike stationary solution of Cahn-Hilliard equation and instability (with Peter W Bates, E Norman Dancer)
     (Advance in Differential Equations, Vol. 4, No. 1, pg. 1-69, 1999)

4.  Exact multiplicity of positive solutions for a class of semilinear problem:II  (with Tiancheng Ouyang)
     (Journal of Differential Equations,Volume 158, No. 1, pg. 94-151, 1999)

5.   Morse indices and Exact multiplicity of solutions to Semilinear Elliptic Problems(with Junping Wang)
     (Proceedings of American Mathematics Society, Vol. 127,  No. 12, pg. 3685-3695, 1999)

6.   Persistence and Bifurcation of Degenerate Solutions
     (Journal of Functional Analysis,Vol 169, No. 2, pg. 494-531, 1999)

7.   Blow-up Points of  Solution Curves for a Semilinear Problem 
     (Topological Methods in Nonlinear Analysis, Vol 15, No.2, pg. 251-266, 2000.)

8.   Instability and exact multiplicity of solutions of semilinear equations, (with P. Korman)
     (Electronic Journal of Differential Equations,  Conf. 05, pg. 311-322, 2000. )

9.   Exact Multiplicity of solutions for classes of problems with concave-convex nonlinearity(with Ratnasingham Shivaji)
      (Discrete and Continuous Dynamical Systems, Series A, Vol 7, No. 3, pg. 559-571, 2001)

10.  New exact multiplicity results with an application to a population model (with Phil Korman)
       (Proceedings of Royal Society of Edinburgh, Series A Vol 13, no. 5, pg. 1167--1182, 2001).

11.   Exact Multiplicity of Solutions to Superlinear and Sublinear Problems
        (Nonlinear Analysis: Theory, Methods & Applications Vol 50, no. 5, pg. 665--687, 2002)

12.  Saddle solutions of the balanced bistable diffusion equation
       (Communications on Pure and Applied Mathematics Vol 55, no. 7, pg. 815--830, 2002)

13.   Global Bifurcation of Semilinear Neumann Boundary Problem 
        (Transactions of American Mathematics Society, Vol 354, no. 8, pg. 3117-3154, 2002)

14.   Existence and instability of spike layer solutions to singular perturbation problems (with Peter W. Bates)
        (Journal of Functional Analysis, Vol 196, no. 2, pg. 429-482, 2002)

15.   Diffusive Logistic equation with constant effort harvesting, I: Steady States (with Shobha Oruganti, Ratnasingham Shivaji)
        (Transactions of American Mathematics Society, Vol 354, no. 9, pg. 3601-3619, 2002)

16.   Exact Multiplicity of positive solutions to superlinear problems 
        (Electronic Journal of Differential Equations,  Conf. 10, pg. 257-265, 2002)

17.   Logistic Equation with the p-Laplacian and Constant Yield Harvesting (with Shobha Oruganti, Ratnasingham Shivaji)
       (Abstract and Applied Analysis, 2004, No. 9, pg. 723--727)

18.   A radially symmetric anti-maximum principle and applications to fishery management models
        (Electronic Journal of Differential Equations, Vol. 2004, No. 27, pg. 1-13, 2004)

19.   Positive Solutions of Elliptic Equations with Singular Nonlinearity (with Miaoxin Yao)
        (Electronic Journal of Differential Equations. Vol. 2005, No.4, pg. 1-11, 2005)

20.   On Lane-Emden type systems (with Phil Korman)
        (Discrete and Continuous Dynamical Systems, Proceedings of 5th AIMS International  Conference on
           Dynamic Systems and Differential  Equations, pg. 510-517, 2005.)

21.   Semilinear elliptic equations with generalized cubic nonlinearities (with Ratnasingham Shivaji)
        (Discrete and Continuous Dynamical Systems, Proceedings of 5th AIMS International  Conference on
           Dynamic Systems and Differential  Equations, pg. 798-805, 2005.)

22.   Bifurcation Diagrams of Population Models with Nonlinear Diffusion (with Young He Lee, Lena Sherbakov, Jackie Taber)
       (Journal of Computational and Applied Mathematics, Vol. 194, no. 2, 357--367, 2006.)

23.   A new proof of anti-maximum principle via a bifurcation approach
       (Results of Mathematics, Vol. 48, No. 1-2, pg. 162--167, 2005)

24.  Some Recent Results on Diffusive Predator-prey Models in Spatially Heterogeneous Environment (with Yihong Du)
      (Nonlinear Dynamics and Evolution Equations, Fields Institute Communications, Vol 48, American Mathematical Society, 95--135, 2006)

25.  Uniqueness of positive solution to sublinear semipositone problem (with E Norman Dancer)
       (Bulletins of London Mathematical Society, Vol. 38, no. 6, 1033--1044, 2006.)

26.   Diffusive population models with Allee effects (with Ratnasingham Shivaji)
        (Journal of Mathematical Biology, Vol. 52, no. 6, 807--829, 2006)

27.  Spatially Heterogeneous Predator-Prey Model with Protect Zone for Prey(with Yihong Du)
       (Journal of Differential Equations, Vol. 229, no. 1, 63--91, 2006)

28.  Hair-Triggered Instability of Radial Steady States, Spread and Extinction in Semilinear Heat Equations. (with Xuefeng Wang)
       (Journal of Differential Equations, Vol 231, no. 1, 235--251, 2006)

29.  Allee Effect and Bistability in a Spatially Heterogeneous Predator-Prey Model (with Yihong Du)
       (to appear in Transactions of American Mathematics Society)

30.   Exact multiplicity of solutions and S-shaped bifurcation curve for a class of semilinear elliptic equations
        (with Yuhua Zhao, Yuwen Wang) (to appear in Journal of Mathematical Analysis and Applications)

31.   Uniqueness of positive solution for a class of semilinear elliptic systems.
       (with Renhao Cui, Yuwen Wang) (to appear in Nonlinear Analysis: Theory, Methods & Applications).

32.   Exact multiplicity of positive solutions for a singular equation in unit ball. (with Tiancheng Ouyang, Miaoxin Yao) (Submitted)
33.  Optimal Spatial Harvesting Strategy and Symmetry-Breaking (with Kazuhiro Kurata)  (Submitted)
34.  The role of higher vorticity moments in a variational formulation of the Barotropic Vorticity Model on a rotating sphere (with Chjan Lim) (Submitted)
35.  Exact multiplicity of boundary blow-up solutions for bistable equation (with Shin-Hwa Wang) (Submitted)
36.  Structure of the solution set of semilinear elliptic equations with asymptotic linear nonlinearity. (with Jia Duo, Yuwen Wang) (Submitted)
37.  Existence and nonexistence of positive solutions of semilinear elliptic equation with inhomogeneous strong Allee effect (with Guanqi Liu, Yuwen Wang) (Submitted)
38.  Imperfect transcritical and pitchfork Bifurcations (with Ping Liu, Yuwen Wang) (Submitted)
39.  Diffusion-Driven Instability and Bifurcation in the Lengyel-Epstein System (with Fengqi Yi, Junjie Wei)  (Submitted)
40.  Dynamics of a reaction-diffusion system of autocatalytic chemical reaction (with Jifa Jiang) (Submitted)

Papers in Refereed Conference Proceedings

1.  A bifurcation approach to the exact multiplicity of semilinear elliptic equations(with Tiancheng Ouyang)
     (Proceedings of International Conference on Dynamic Systems and Differential Equations,
     Edited by W.X. Chen and S.C. Hu, Discrete and Continuous Dynamical Systems, 1996, Volume 2, pg. 162--173)
2.  Exact Multiplicity of Solutions and global bifurcation of $\Delta u+\lambda f(u)=0$(with Tiancheng Ouyang)
     (Proceedings of US-Chinese Conference on Differential equations and Applications,
     Edited by P.W. Bates, S-N. Chow, K. Lu and X. Pan, World Scientific, Singapore, 1998, pg. 356--363)
3.  Global bifurcations of concave semipositone problems. (with Ratnasingham Shivaji) (pdf file, 144K, 17 pages)
     (Advances in Evolution Equations: Proceedings in honor of J.A.Goldstein's 60th birthday
     Edited by G.R. Goldstein, R. Nagel, and S. Romanelli, Marcel Dekker, Inc., New York, Basel, 2003, pg. 385--398.)
4.  Multi-Parameter Bifurcation and Applications, (pdf file, 122K, 10 pages)
     (ICM 2002 Satellite Conference on Nonlinear Functional Analysis: Topological Methods, Variational Methods and Their Applications
     Edited by H. Brezis, K.C. Chang, S.J. Li and P. Rabinowitz, World Scientific, Singapore, 2003, pg.211--222.)
5.  Asymptotic Spatial Patterns and  Entire Solutions of Semilinear Elliptic Equations (pdf file, 130K, 9 pages)
     (Proceedings of the Ryukoku Workshop 2003)  

Expository articles

1. Mathematical problems in celestial mechanics---From Newton to Poincar\'{e}, (in Chinese)
    (Kexue (Science) Magazine,  Vol 53, No. 5, 38-40, 2001).
2. Painlev\'{e} conjecture and N-body problem, (in Chinese).
    (Kexue (Science) Magazine,  Vol 53, No. 6, 20-23, 2001).
3. Electronic publishing of mathematical research papers, (in Chinese)
    (Kexue (Science) Magazine, Vol 54, No. 3, 55--58, 2002).
4.  Life's other secret (in Chinese)
     (Kexue (Science) Magazine, Vol 57, No. 6, 28--32, 2005)

Papers in preparation

1. Global Bifurcation of steady state solutions of a convective reaction-diffusion equation
2. Nucleating solutions of Cahn-Hilliard equation
3. A Remark on the Applications of Bifurcation Theory  to Problems with Nonlinear Boundary Conditions (with Xuefeng Wang)

Junping Shi's Ph. D Dissertation Topics in Nonlinear Elliptic Equations
1. Bifurcation Theory of Nonlinear Elliptic Equations
2. Spike Layer Solutions of the Cahn-Hilliard Equation
(pdf file, 1029K)

Lecture notes and book manuscripts:


Reaction diffusion equations and mathematical biology. Undergraduate Lecture Notes, (2004). pp. 1--93.

Lecture Notes on solution set of semilinear elliptic equations. (Lectures given in Harbin Normal
University, China and Tokyo Metropolitan University, Japan), (2005). pp. 1--114.

Very rough lecture note on bifurcation of elliptic systems (Lectures given in Harbin Normal University, China, June 2006)  (2006). pp 1--33. (in Chinese)


If you need some hard copies of above papers, please e-mail me.

This page is created by Junping Shi in June 18th, 1996, updated by Junping Shi in September 4th, 2006.
Any comment? email me !