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 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, 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).

(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 Mathematic

59.

(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)

(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)

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)

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)

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)

- Optimal
Spatial Harvesting
Strategy and Symmetry-Breaking (pdf) June 2006

- Bistable
dynamics in
autocatalytic chemical reactions (pdf) June 2006

- Bistability
in chemical reactions and
predator-prey systems (pdf) March 2006

- A
variational problem in climate dynamics
(powerpoint) April 2005

- Allee
Effect and
Bistability in Spatially Heterogeneous Predator-Prey Models (pdf)
April 2005

- Isothemal
Balls in an autocatalytic
chemical reaction (pdf) Feb 2005

- Bistability,
Allee Effect and
Threshold Manifold in Structured Population Models (powerpoint)
Jan 2005

- Pattern formations in Mathematical Biology (undergraduate lecture, partly in Chinese) (Powerpoint) May 2004
- Reaction-diffusion models with Allee effect (Powerpoint) May 2004
- Asymptotic Spatial Patterns and Entire Solutions (pdf) June 2003

This page is created by Junping
Shi in June 18th, 1996, updated by Junping
Shi in Aug. 12th, 2009.

Any comment? email me !