Publications and Presentations by Junping Shi

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, Volume 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, Volume 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, Volume 127,  No. 12, pg. 3685-3695, 1999)

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

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

8.   Instability and exact multiplicity of solutions of semilinear equations, (with P. Korman)
     (Electronic Journal of Differential EquationsConf. 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, Volume 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 Volume 13, no. 5, pg. 1167--1182, 2001).

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

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

13.   Global Bifurcation of Semilinear Neumann Boundary Problem 
        (Transactions of American Mathematics Society, Volume 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, Volume 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, Volume 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)
       (Transactions of American Mathematics Society, Vol. 359, no. 9, 4557--4593, 2007)

30.   Exact multiplicity of solutions and S-shaped bifurcation curve for a class of semilinear elliptic equations
        (with Yuhua Zhao, Yuwen Wang) (Journal of Mathematical Analysis and Applications, Vol 331, no. 1, 263--278, 2007)

31.   Uniqueness of positive solution for a class of semilinear elliptic systems.
       (with Renhao Cui, Yuwen Wang) (Nonlinear Analysis: Theory, Methods & Applications, Vol 67, No.6, 1710--1714, 2007)

32.   Diffusion-Driven Instability and Bifurcation in the Lengyel-Epstein System (with Fengqi Yi, Junjie Wei) 
        (Nonlinear Analysis: Real World Applications, 9 (2008), no. 3, 1038–1051)

33.   Exact multiplicity of boundary blow-up solutions for bistable equation (with Shin-Hwa Wang)
        (Computers & Mathematics with Applications, 54 (2007), no. 9-10, 1285–1292.)

34.   Dynamics of a reaction-diffusion system of autocatalytic chemical reaction (with Jifa Jiang)
        (Discrete and Continuous Dynamical Systems, Series A, 21 (2008), no. 1, 245–258.)

35.   Imperfect transcritical and pitchfork Bifurcations (with Ping Liu, Yuwen Wang)
        (Journal of Functional Analysis, 251 (2007), no. 2, 573--600.)

36.   Stationary Pattern of a Ratio-dependent Food Chain Model with Diffusion (with Rui Peng, Mingxin Wang)
        (SIAM Journal of Applied Mathematics, 67 (2007), no. 5, 1479--1503)

37.   Structure of the solution set of semilinear elliptic equations with asymptotic linear nonlinearity. (with Jia Duo, Yuwen Wang)
        (Nonlinear Analysis: Theory, Methods & Applications, 69 (2008), no.8,  2369--2378)

38.   Optimal Spatial Harvesting Strategy and Symmetry-Breaking (with Kazuhiro Kurata)
        (Applied Mathematics and Optimization, 58 (2008), no. 1, 89--110.)

39.  Global asymptotical behavior of the Lengyel-Epstein reaction-diffusion system (with Fengqi Yi, Junjie Wei)
       (Applied Mathematics Letters, 22 (2009), no. 1, 52--55)

40.   On Stationary Patterns of a Reaction-diffusion Model with Autocatalysis and Saturation Law (with Rui Peng, Mingxin Wang)
       (Nonlinearity, 21 (2008), no. 7, 1471–1488.)

41.   Exact multiplicity of solutions to perturbed logistic type equations on a symmetric domain.  (with Ping Liu, Yuwen Wang)
       (Science in China Series A: Mathematics, 51 (2008), no. 10, 1753--1762. (Chinese edition: 38 (2008) no. 8, 930--939. Chinese version of the paper)

42.   Bifurcation and Spatiotemporal Patterns  in a Homogeneous Diffusive Predator-Prey System. (with Fengqi Yi, Junjie Wei)
        (Journal of Differential Equations, 246 (2009) no. 5, 1944--1977)

43.  The role of higher vorticity moments in a variational formulation of the Barotropic Vorticity Model on a rotating sphere (with Chjan Lim)
       (Discrete and Continuous Dynamical Systems, Series  B, 11 (2009) no. 3, 717--740).

44.  Bistability dynamics in some structured  ecological models (with Jifa Jiang)
       (a chapter in Spatial Ecology, a book published by CRC Press, 2009)

45.  On global bifurcation for quasilinear elliptic systems on bounded domains(with Xuefeng Wang)
        (Journal of Differential Equations, 246 (2009) no.7, 2788--2812)

46.  Bifurcation in infinite dimensional spaces and applications in spatiotemporal biological and chemical models.
       (Frontier of Mathematics in China, 4, (2009), no. 3, 407--424.)

47.  Relaxation oscillator profile of limit cycle in  predator-prey system. (with Sze-Bi Hsu)
       (Discrete and Continuous Dynamical Systems, Series  B, 11 (2009) no. 4, 893--911).

48.  Non-existence of Non-constant Positive Steady States of Two Holling Type-II Predator-prey Systems: Strong Interaction Case (with Rui Peng)
       (Journal of Differential Equations, 247, (2009), no. 3, 866--886. )

49.  Hopf Bifurcations  in a Reaction-Diffusion Population Model with Delay Effect (with Ying Su, Junjie Wei)
      (Journal of Differential Equations, 247, (2009), no. 5, 1156--1184.)

50.  Bifurcation analysis in a delayed diffusive Nicholson's blowies equation (with Ying Su, Junjie Wei)
       (Nonlinear Analysis: Real World Applications, 11, (2010), no. 3, 1692--1703.)

51.  Classification of four-body central configurations with three equal masses. (with Zhifu Xie)
       (Journal of Mathematical Analysis and Applications, 363, (2010), no. 2, 512--524.)

52.  Existence and nonexistence of positive solutions of semilinear elliptic equation with inhomogeneous strong Allee effect (with Guanqi Liu, Yuwen Wang)
       (Applied Mathematics and Mechanics, 30, (2009), no. 11, 1461--1468. (Chinese edition: 30, (2009), 11, 1374-1380).)

53.   Predator-prey system with strong Allee effect in prey (with Jinfeng Wang, Junjie Wei)
        (to appear in Journal of Mathematical Biology)

54.  Exact multiplicity of solutions to a diffusive logistic equation with harvesting.(with Yanan Wang, Yuwen Wang)
       (Applied Mathematics and Computation, 216, (2010), no. 5,1531--1537)

55.  Existence, Uniqueness and Stability of Positive Solutions to Sublinear Elliptic Systems (with Jann-Long Chern, Chang-Shou Lin, Yong-Li Tang)
       (to appear in Proceedings of Royal Society of Edinburgh, Series A)

56.  Complete controllability of impulsive stochastic integro-differential systems (with Lijuan Shen, Jitao Sun)
       (Automatica, 46, (2010), no. 6, 1068--1073)

57.   Periodic solutions of logistic type population model with harvesting (with Ping Liu, Yuwen Wang)
        (Journal of Mathematical Analysis and Applications, 369, (2010), no.2, 730--735)

58.   Existence and Uniqueness of positive solutions for a class of semilinear elliptic systems (with Renhao Cui, Yuwen Wang)
        (to appear in  Acta Mathematica Sinica)

On the Uniqueness and Structure of Solutions to a Coupled Elliptic System (with Zhi-You Chen, Jann-Long Chern, Yong-Li Tang)
       (Journal of Differential Equations, 249, (2010), no. 12, 3419--3442)

60.  Exact multiplicity of positive solutions for a singular equation in unit ball. (with Tiancheng Ouyang, Miaoxin Yao) (preprint)
61.  Cross-diffusion induced instability and stability in reaction-diffusion systems (with Zhifu Xie, Kristina Little) (Submitted)
62.  Smoothness of crossing curves (with Zhifu Xie). 
63.  Bifurcations of Patterned Solutions in Diffusive Lengyel-Epstein System of CIMA Chemical Reaction (with Jiayin Jin, Junjie Wei, Fengqi Yi) (submitted)
64.  Bifurcation diagrams of coupled Schrodinger Equations (with Michael Essman) (submitted)
65.  Three-pool model of calcium signaling (with Daniel Hariprasad, Meagen Herald, Jianjun Paul Tian) (submitted)
65.  A model for emergence of high pathogenicity avian influenza virus from outbreaks with low pathogenicity avian influenza virus (with Jianjun Paul Tian, Xiaojie Hou) (submitted)
67.  Nonexistence of periodic orbits for predator-prey system with strong Allee effect in prey population (with Jinfeng Wang, Junjie Wei) (submitted)
68.  A double saddle-node bifurcation theorem (with Ping Liu, Yuwen Wang) (submitted)
69.  A Note on Hopf bifurcations in a delayed diffusive Lotka-Volterra predator-prey system (with Shanshan Chen, Junjie Wei) (submitted)
70.  Global stability of multigroup epidemic model with group mixing and nonlinear incidence rates (with Ruoyan Sun) (submitted)
71.  Existence and Uniqueness of Steady State Solutions of a Nonlocal Diffusive Logistic Equation (with Linan Sun, Yuwen Wang) (submitted)
72.  Global Stability and Hopf Bifurcation in a Delayed Diffusive Leslie-Gower Predator-prey System (with Shanshan Chen, Junjie Wei) (submitted)
73.  Bistability in a Differential Equation Model of Oyster Population and Sediment Volume. (with William Jordan-Cooley, Romuald N. Lipcius, Leah Shaw, Jian Shen) (submitted)
74.  Dynamics and Pattern Formation in a Diffusive Predator-Prey System with Strong Allee Effect in Prey (with Jinfeng Wang, Junjie Wei) (submitted)
75.  The Effect of Delay on a  Diffusive Predator-Prey System with Holling Type-II Predator Functional Response, (with Shanshan Chen, Junjie Wei) (submitted)
76.  Hopf bifurcation and Turing instability in the reaction-diffusion Holling-Tanner predator-prey model, (with Xin Li, Weihua 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) MagazineVol 53, No. 5, 38-40, 2001).
2. Painlev\'{e} conjecture and N-body problem, (in Chinese).
    (Kexue (Science) MagazineVol 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)

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)

Lecture Notes on Differential Equations and Mathematical Biology (Lecture given in Harbin Institute of Technology, China, May 2009)
(2009). pp 1--92. (in Chinese)


  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
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 Aug. 12th, 2009.
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