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)
(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)
(to appear in Nonlinear
Analysis: Theory, Methods & Applications)
38. Optimal
Spatial
Harvesting Strategy and Symmetry-Breaking (with Kazuhiro
Kurata)
(to appear in Applied Mathematics and Optimization)
39. Global asymptotical behavior
of the Lengyel-Epstein
reaction-diffusion system (with Fengqi Yi, Junjie Wei)
(to appear in Applied Mathematics Letters)
40. On
Stationary Patterns of a Reaction-diffusion Model
with Autocatalysis and Saturation Law (with Rui Peng, Mingxin Wang)
(to appear in Nonlinearity)
41. Exact
multiplicity of solutions to perturbed logistic
type equations on a symmetric domain. (with Ping Liu, Yuwen
Wang)
(to appear in Science in China Series A: Mathematics)
(Chinese version of the paper)
42. Exact
multiplicity of positive solutions for a singular equation in unit ball.
(with Tiancheng
Ouyang, Miaoxin
Yao) (preprint)
43. The
role of higher vorticity moments
in a variational
formulation of the Barotropic Vorticity Model on a rotating sphere
(with Chjan Lim) (Submitted).
44. Existence
and nonexistence of
positive solutions of semilinear elliptic equation with inhomogeneous
strong Allee effect (with Guanqi Liu, Yuwen Wang) (Submitted)
45. Cross-diffusion
induced instability
and stability in reaction-diffusion systems (with Zhifu Xie,
Kristina Little) (Submitted)
46. Smoothness
of crossing curves (with
Zhifu Xie)
47. Quasilinear Elliptic
Systems with Nonlinear Boundary Conditions Have Zero Fredholm Index,
and Application to Global Bifurcation Theory (with Xuefeng Wang)
(submitted)
48. Relaxation oscillator profile of
limit cycle in predator-prey system. (with Sze-Bi Hsu)
(submitted)
49. Bifurcation and Spatiotemporal
Patterns in a Homogeneous Diffusive Predator-Prey System.
(with Fengqi Yi, Junjie Wei) (submitted)
50. Bistability dynamics in
some structured ecological models (with Jifa Jiang)
(submitted)
51. Exact multiplicity of solutions to
a diffusive logistic equation with harvesting.(with Yanan Wang,
Yuwen Wang) (submitted)
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)
This page is created by Junping
Shi in June 18th, 1996, updated by Junping
Shi in September 4th, 2006.
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