Shin-Hwa Wang Professor of Mathematics Department of Mathematics National Tsing Hua University, Taiwan, Republic of China § E-Mail: shwang@math.nthu.edu.tw § Phone: (886) 3 - 5731042 § Fax: (886) 3 - 5723888 |
RESEARCH INTERESTS
§ Differential Equations
EDUCATION
§ 1988 PH.D. State University of New York at
Buffalo, U.S.A.
§ 1986 M.S. State University of New York at
Buffalo, U.S.A.
§ 1981 B.S. National Taiwan University,
Taipei, Taiwan
PROFESSIONAL EMPLOYMENTS
§ 1994/08 - Professor, Department of Mathematics,
National Tsing Hua University, Republic of China
§ 1988/09 - 1994/07 Associate Professor,
Department of Mathematics, National Tsing Hua University, Republic of China
§ 1984/09 - 1988/06 Teaching Assistant,
Department of Mathematics, State University of New York at Buffalo, U.S.A.
§ 1983/07 - 1984/06 Research Assistant,
Institute of Mathematics, Academia Sinica
MEMBER
§ The Mathematical Society of the Republic of China
STUDENTS
§ 80 學年度 數學所 碩士 龍道民
『Bifurcation of positive solutions of a
generalized Gelfand problem』
§ 80 學年度 應數所 碩士 謝坤家
『Bifurcation of positive solutions of
some classes of nonlinear two-point boundary value problems』
§ 81 學年度 數學所 碩士 厲復平
『Bifurcation of an equation from
catalysis theory』
§ 86 學年度 數學所 碩士 劉月增
『On the bifurcation curve of boundary
blow-up solutions of a boundary value problems』
§ 88 學年度 數學所 碩士 謝明廷
『Necessary and sufficient conditions
for the existence of solutions of a boundary blow-up problem』
§ 89 學年度 數學所 碩士 卓益安
『An explicit formula and asymptotic
behaviors of bifurcation curve of a boundary blow-up problem』
§ 90 學年度 數學所 碩士 黃佩瑜
『On necessary and sufficient conditions
for the existence of solutions of a p-laplacian boundary blow-up problem』
§ 90 學年度 數學所 碩士 余彩璃
『Asymptotic behaviors of the
bifurcation curve for a p-laplacian boundary blow-up problem』
§ 91 學年度 數學所 碩士 李信儀
『On necessary and sufficient conditions
for the existence of dead core solutions of a two point boundary value problem』
§ 91 學年度 數學所 碩士 夏文茵
『The structure of the solution set of a
generalized ambrosetti-brezis-cerami problem in one space variable』
§ 91 學年度 數學所 博士 葉宗鑫
『Structure of the solution set of a
generalized Ambrosetti- Brezis-Cerami problem in one space variable』
§ 92 學年度 數學所 碩士 葉秋萍
『On necessary and sufficient conditions
for the existence of dead core solutions of a two point p-laplacian boundary
value problem』
§ 94學年度數學所/碩士 劉仲益
『A complete claasification of
bifurcation diagrams of a p-Laplacian Dirichlet problem』
§ 94學年度數學所/碩士 王鳳麟
『A complete classification of
bifurcation diagrams of a p-Laplacian Dirichlet problem. II. Generalized
nonlinearities』
§ 95學年度數學所/碩士 黃韋強
『On the Evolution and Qualitative
Behaviors of Bifurcation Curves for a Boundary Value Problem. II』
§ 97學年度數學所/碩士 洪國智
『Global bifurcation and exact
multiplicity of positive solutions for some classes of p-Laplacian
multiparameter problems』
§ 98學年度 數學所 碩士 曾至均
『Chih-Chun Tzeng, Kuo-Chih Hung and Shin-Hwa Wang*, 2012,『Global bifurcation and exact multiplicity of positive solutions for a positone problem with cubic nonlinearity』
§ 99學年度 數學所 碩士 余建賢
『Existence of a double S-shaped bifurcation curve with six positive solutions for a combustion problem』
§ 99 學年度 數學所 碩士 莊家豪
『On exact multiplicity and bifurcation diagrams of positive solutions of a one-dimensional prescribed mean curvature problem』
§ 100學年度 數學所 碩士 陳志淵
『S-shaped bifurcation curves in a combustion problem with general Arrhenius reaction-rate laws』
§ 105學年度 數學所 碩士 郭達昌
『Classification and evolution of bifurcation curves for a Dirichlet-Neumann boundary value problem and its application』
§ 106學年度 數學所 碩士 孫耀楠
『Structures and evolution of bifurcation curves for a one-dimensional semipositone Dirichlet problem』
REFERRED JOURNAL PAPERS: PDF Files
1. A correction for a paper by J. Smoller and A. Wasserman, Journal
of Differential Equations 77 (1989), 199--202. (SCI) PDF
2. On positive solutions of some semilinear elliptic equations, Journal
of the Australian Mathematical Society (Series A) 50 (1991), 343--355. (with N.
D. Kazarinoff) (SCI) PDF
3. Bifurcation and stability of positive solutions of a two-point
boundary value problem, Journal of the Australian Mathematical Society (Series
A) 52 (1992), 334--342. (with N. D. Kazarinoff) (SCI) PDF
4. Bifurcation of steady-state solutions of a scalar
reaction-diffusion equation in one space variable, Journal of the Australian
Mathematical Society (Series A) 52 (1992), 343--355. (with N. D. Kazarinoff)
(SCI) PDF
5. Bifurcation of positive solutions of generalized nonlinear
undamped pendulum problems, Bulletin of the Institute of Mathematics, Academia
Sinica 21 (1993), 211--227. PDF
6. Remarks on the monotonicity and convexity of the time maps of
some two-point boundary value problems, Chinese Journal of Mathematics 21
(1993), 259--269. PDF
7. On the time map of a nonlinear two-point boundary value problem,
Differential and Integral Equations 7 (1994), 49--55. PDF
8. Positive solutions for a class of nonpositone problems with
concave nonlinearities, Proceedings of the Royal Society of Edinburgh 124A
(1994), 507--515. (SCI) PDF
9. On S-shaped bifurcation curves, Nonlinear Analysis, Theory,
Methods & Applications 22 (1994), 1475--1485. (SCI) PDF
10.Bifurcation of an equation from catalysis theory, Nonlinear
Analysis, Theory, Methods & Applications 23 (1994), 1167--1187. (with F.-P.
Lee) (SCI) PDF
11.Bifurcation of an equation arising in porous medium combustion,
IMA Journal of Applied Mathematics 56 (1996), 219--234. (SCI) PDF
12.Rigorous analysis and estimates of S-shaped bifurcation curves
in a combustion problem with general Arrhenius reaction-rate laws, Proceedings
of the Royal Society of London, Series A 454 (1998), 1031--1048. (SCI) PDF
13.Existence and multiplicity of boundary blow-up nonnegative
solutions to two-point boundary value problems, Nonlinear Analysis, Theory,
Methods & Applications 42 (2000), 139--162. (SCI) PDF
14.Existence and multiplicity of an equation from pool boiling on
wires, Quarterly of Applied Mathematics 58 (2000), 331--354. (SCI) PDF
15.An exact multiplicity theorem involving concave-convex
nonlinearities and its application to stationary solutions of a singular
diffusion problems, Nonlinear Analysis, Theory, Methods & Applications 44
(2001), 469--486. (with D.-M. Long) (SCI) PDF
16.An explicit formula of the bifurcation curve for a boundary
blow-up problem, Dynamics of Continuous, Discrete and Impulsive Systems Ser. A
Math. Anal. 10 (2003), 431--446. (with Y.-T. Liu and I-A. Cho) (SCI Expanded) PDF
17.Exact multiplicity results for a p-Laplacian problem with
conacve-convex-concave nonlinearities, Nonlinear Analysis, Theory, Methods
& Applications 53 (2003), 111--137. (with I. Addou) (SCI) PDF
18.Exact multiplicity and ordering properties of positive solutions
of a p-Laplacian Dirichlet problem and their applications, Journal of
Mathematical Analysis and Applications 287 (2003), 380--398. (with T.-S. Yeh)
(SCI) PDF
19.On the exact structure of positive solutions of an
Ambrosetti-Brezis-Cerami problem and its generalization in one space variable,
Differential and Integral Equations 17 (2004), 17--44. (with T.-S. Yeh) PDF
20.A complete classification of bifurcation diagrams of a Dirichlet
problem with concave-convex nonlinearities, Journal of Mathematical Analysis
and Applications 291 (2004), 128--153. (with T.-S. Yeh) (SCI) PDF
21.Exact multiplicity results for a p-Laplacian positone problem
with concave-convex-concave nonlinearities, Electronic Journal of Differential
Equations 2004 (2004), 1--25. (with I. Addou) PDF
22.Shape and structure of the bifurcation curve of a boundary
blow-up problem, Taiwanese Journal of Mathematics 9 (2005), 201--214. (with
Y.-T. Liu) (SCI) PDF
23.Explicit necessary and sufficient conditions for the existence
of a dead core solution of a p-Laplacian steady-state reaction-diffusion
problem, Discrete and Continuous Dynamical Systems - Series A, Supplement
Volume, 2005, 587--596. (with S.-Y. Lee and C.-P. Ye) (SCI) PDF
24.The structure of the solution set of a generalized
Ambrosetti-Brezis-Cerami problem in one space variable, Journal of Mathematical
Analysis and Applications 313 (2006), 441--460. (with W.-Y. Hsia and T.-S. Yeh)
(SCI) PDF
25.A complete classification of bifurcation diagrams of a
p-Laplacian Dirichlet problem, Nonlinear Analysis, Theory, Methods &
Applications 64 (2006), 2412--2432. (with T.-S. Yeh) (SCI) PDF
26.On the evolution and qualitative behaviors of bifurcation curves
for a boundary value problem, Nonlinear Analysis, Theory, Methods &
Applications 67 (2007), 1316--1328. (SCI) PDF
27.A complete classification of bifurcation diagrams of a
p-Laplacian Dirichlet problem, Journal of Mathematical Analysis and
Applications 330 (2007), 276--290. (with S.-Y. Lee, J.-Y. Liu, and C.-P. Ye)
(SCI) PDF
28.Exact structure of positive solutions for a p-Laplacian problem
involving singular and superlinear nonlinearities, Rocky Mountain Journal of
Mathematics 37 (2007), 689--708. (with T.-S. Yeh) (SCI Expanded) PDF
29.Exact multiplicity of boundary blow-up solutions for a bistable
problem, Computers and Mathematics with Applications 54 (2007), 1285-1292.
(with J. Shi) (SCI) PDF
30.Exact multiplicity of solutions and S-shaped bifurcation curves
for the p-Laplacian perturbed Gelfand problem in one space variable, Journal of
Mathematical Analysis and Applications, 342 (2008), 1175-1191. (with Tzung-Shin
Yeh) (SCI) PDF
31.On the evolution and qualitative behaviors of bifurcation curves
for a boundary value problem. II, Nonlinear Analysis, Theory, Methods &
Applications. (2008) (with W.-C. Huang) (SCI) PDF
32.Explicit necessary and sufficient conditions for the existence
of nonnegative solutions of a p-Laplacian boundary blow-up problem, Taiwanese
Journal of Mathematics, 13 (2009). (with Pei-Yu Huang and Ming-Ting Shieh)
(SCI) PDF
33.A theorem on reversed S-shaped bifurcation curves for a class of
boundary value problems and its application, Nonlinear Analysis 71 (2009),
126-140. (with Tzung-Shin Yeh) (SCI) PDF
34.A complete classification of bifurcation diagrams of classes of
a multiparameter Dirichlet problem with concave-convex nonlinearities, Journal
of Mathematical Analysis and Applications, 349 (2009), 113-134. (with Kuo-Chih
Hung) (SCI) PDF
35.A
complete classification of bifurcation diagrams of classes of multiparameter
p-Laplacian boundary value problems, Journal of Differential Equations, 246
(2009), 1568-1599. (with Kuo-Chih Hung) (SCI) PDF
36.Classification
of bifurcation diagrams of a p-Laplacian Dirichlet problem with
examples, Journal of Mathematical Analysis and Applications, 369 (2010),
188-204. (with Tzung-Shin Yeh) (SCI) PDF
37.Bifurcation
diagrams of a p-Laplacian Dirichlet problem with Allee effect and an
application to a diffusive logistic equation with predation, Journal of Mathematical Analysis and
Applications, 375 (2011), 294-309. (with Kuo-Chih Hung) (SCI) PDF
38.Classification
and evolution of bifurcation curves for a multiparameter p-Laplacian Dirichlet
problem, Nonlinear Analysis,
74 (2011), 3589-3598. (with Kuo-Chih Hung) (SCI) PDF
39.A
theorem on S-shaped bifurcation curve for a positone problem with
convex-concave nonlinearity and its applications to the perturbed Gelfand
problem, Journal of Differential Equations, 251 (2011), 223-237.
(with Kuo-Chih Hung) (SCI) PDF
40.A complete classification of bifurcation diagrams of a p-Laplacian Dirichlet problem. II. Generalized nonlinearities,Taiwanese Journal of Mathematics, 16 (2012), 1265-1291. (with Feng-Lin Wang) (SCI) PDF
41.On the existence of a double S-shaped bifurcation
curve with six positive solutions for a combustion problem, Journal of Mathematical Analysis and Applications, 392 (2012), 40-54. (K.-C. Hung and C.-H.
Yu) (SCI) PDF
42.Global bifurcation and exact multiplicity of
positive solutions for a positone problem with cubic nonlinearity,Journal of Differential Equations, 252 (2012), 6250-6274. (with C.-C. Tzeng and K.-C. Hung) (SCI) PDF
43.Classification of bifurcation diagrams of a
p-Laplacian nonpositone problem, Communications on
Pure and Applied Analysis, 12
(2013), 2297-2318. (with P.-C. Huang and T.-S. Yeh) (SCI) PDF
44.Global bifurcation and exact multiplicity of
positive solutions for a positone problem with cubic nonlinearity and their
applications, Transactions of the American Mathematical Society, 365 (2013), 1933-1956. (with Kuo-Chih Hung)
(SCI) PDF
45.S-shaped
and broken S-shaped bifurcation diagrams for a multiparameter spruce budworm
population problem in one space dimension, Journal of Differential Equations, 255 (2013), 812-839. (with
Tzung-Shin Yeh) (SCI) PDF
46.Global bifurcation diagrams and exact multiplicity of positive solutions for a one-dimensional prescribed mean curvature problem arising in MEMS, Nonlinear Analysis, 89 (2013), 284-298. (with Y.-H. Cheng and K.-C. Hung) (SCI) PDF
47.Exact multiplicity and bifurcation diagrams of positive solutions of a one-dimensional prescribed mean curvature problem, Journal of Differential Equations, 257 (2014), 3272-3299. (with Kuo-Chih Hung, Yan-Hsiou Cheng and Chia-Hao Chuang) (SCI) PDF
48.S-shaped bifurcation curves for a combustion problem with general Arrhenius reaction-rate laws, Communications on Pure and Applied Analysis, 13 (2014), 2589-2608. (with Chih-Yuan Chen and Kuo-Chih Hung) (SCI)PDF
49.On S-shaped bifurcation curves for a two-point boundary value problem arising in a theory of thermal explosion, Discrete and Continuous Dynamical Systems, 35 (2015), 4839-4858. (with Shao-Yuan Huang) (SCI)PDF
50.Proof of a conjecture for the one-dimensional perturbed Gelfand problem from combustion theory, Archive for Rational Mechanics and Analysis, 222 (2016), 769-825. (with Shao-Yuan Huang) (SCI)PDF
51.Classification and evolution of bifurcation curves for the one-dimensional perturbed Gelfand equation with mixed boundary conditions, Journal of Differential Equations, 260 (2016), 8358-8387. (with Yu-Hao Liang) (SCI)PDF
52.On the classification and evolution of bifurcation curves for a one-dimensional prescribed mean curvature problem, Differential and Integral Equations, 29 (2016), 631-664. (with Yan-Hsiou Chen and Kuo-Chih Hung) (SCI)PDF
53.A variational property on the evolutionary bifurcation curves for a positone problem with cubic nonlinearity, Taiwanese Journal of Mathematics, 23 (2016), 307-331. (with Shao-Yuan Huang) (SCI)PDF
54.On the classification and evolution of bifurcation curves for a one-dimensional prescribed mean curvature problem with nonlinearity exp(((au)/(a+u))), Nonlinear Analysis, 146 (2016), 161-184. (with Yan-Hsiou Chen and Kuo-Chih Hung) (SCI)PDF
55.A variational property on the evolutionary bifurcation curves for the one-dimensional perturbed Gelfand problem from combustion theory, Electronic Journal of Qualitative Theory of Differential Equations, 94 (2016), 1-21. (with Shao-Yuan Huang) (SCI)PDF
56.A global bifurcation theorem for a positone multiparameter problem and its application, Discrete and Continuous Dynamical Systems, 37 (2017), 5127-5149. (with Kuo-Chih Hung and Shao-Yuan Huang) (SCI)PDF
57.Classification and evolution of bifurcation curves for the one-dimensional perturbed Gelfand equation with mixed boundary conditions II, Electronic Journal of Differential Equations, 2017, No. 61, pp. 1-12. (with Yu-Hao Liang) (SCIE)PDF
58.Classification and evolution of bifurcation curves for a one-dimensional Neumann-Robin problem and its applications, Electronic Journal of Qualitative Theory of Differential Equations, 85 (2018), 1-30. (with Chi-Chao Tsai and Shao-Yuan Huang) (SCI)PDF
59.A global bifurcation theorem for a multiparameter positone problem and its application to the one-dimensional perturbed Gelfand problem, Electronic Journal of Qualitative Theory of Differential Equations, 99 (2019), 1-25. (with Shao-Yuan Huang and Kuo-Chih Hung) (SCI)PDF
60.Classification and evolution of bifurcation curves for a Dirichlet-Neumann boundary value problem and its application, Taiwanese Journal of Mathematics, 23 (2019), 307-331. (with Da-Chang Kuo and Yu-Hao Liang) (SCI)PDF
61.Structures and evolution of bifurcation diagrams for a one-dimensional diffusive generalized logistic problem with constant yield harvesting, Journal of Differential Equations, 269 (2020), 3456-3488. (with Kuo-Chih Hung and Yiu-Nam Suen) (SCI) PDF
62.Classification and evolution of bifurcation curves for a one-dimensional Dirichlet-Neumann problem with a specific cubic nonlinearity, Discrete and Continuous Dynamical Systems, 40 (2020), 1075-1105. (with Yu-Hao Liang) (SCI)PDF
63.Global bifurcation and exact multiplicity of positive solutions of a problem arising in porous-medium combustion, Communications on Pure and Applied Analysis, 20 (2021), 559-582. (with Kuo-Chih Hung) (SCI)PDF