Sze-Bi Hsu

Department of Mathematics

National Tsing-Hua University

Hsinchu, Taiwan 300

Email: sbhsu@math.nthu.edu.tw

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Education

B. S., Tsing-Hua University, Taiwan 1970

ph. D., University of Iowa, 1976

Professional Experience

Instructor, University of Utah, 1976-1979

National Chiao-Tung University

Associate Professor, 1979-1980

Professor, 1980-1985

National Tsing-Hua University

Professor, 1985--

Chairman, Institute of Applied Mathematics, 1987-1990

Dean, College of Science, 1998-2004

  Visiting Professor, University of Maryland, 1986-1987

  Visiting Professor, Emory University, 1990-1991

Visiting Professor, Texas A&M University, 2004-2005

Award

  MOE Science Award, 2005

  MOE National Chair Professor (Feb.1,2011-Jan.31, 2014)

 Tsing-Hua Distinguished  Chair Professor (2011-)

 ROC Mathematical Society Award 2012

 SIAM Fellow 2013

Books

Lectures on Chaotic Dynamical Systems, International Press, 2002 (with Valentine Afraimovich) 

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Ordinary Differential Equations with Applications, Word Scientific Press, 2006 (First edition), 2013 (Second edition).

Lecture Notes

Mathematical Biology for undergraduate students [DOC]

Mathematical Modelling in Biologial Science [PDF]

Introduction to Mathematical Biology Math.380 / 2013 [PDF1] [PDF2][Discrete Logistic Map][1.2 Single Species Growth Discrete Case][1.3 Multiple Species Interactions][1.3Linearization][1.4Two Dimensional Linear System][1.5 Predator Prey Model][1.6 Competition Model][Holling Type II and Epidemics models][MatlabProgram][Discrete Map LPA Model& Baily-Nicholson][Population Genetics1][Population Genetics2][Population Genetics3][Leslie Matrix][Population Genetics Models][Population Genetics2][Genetics and Probability][Modeling of nucleotide substitution]

Journal Articles

I.: Mathematical Biology

II.: Chaotic Vibrating Strings

III.: Mechanics and Gas Dynamics

      I.         Mathematical Biology

  1. Numerical proof for chemostat chaos of Shilnikov type, (with Bo Deng , Maoan Han) to appear in Chaos Deng PDFDeng Bo/ChemoChaos.pdf
  2. The Morbidostat: A Bio-reactor that promotes selection for dry-resistance in bacteria (with Zhenzhen Chen and Ya-Tang Yang) , to appear in SIAM J. Applied Mathematics. PDF
  3. Competition for two essential resources with internal storage and periodic input (with Feng-Bin Wang and Xiaoqiang Zhao) , Differential and Integral Equations(2016) vol29(7-8) p.601-630 PDF
  1. Growth of single phytoplankton species with internal storage in a water column (with Linfeng Mei, Feng-Bin Wang), DCDS-B (2016), p. 607-620 PDF
  2. Dynamics of harmful algae with seasonal temperature variation in the cove-main lake (with Wendi Wang, Feng-Bin Wang) DCDS-B Vol. 21, No.1 (2016) p. 313-335PDF
  3. On a nonlocal reaction-diffusion system modeling the growth of phytoplankton with cell quota structure (with Linfeng Mei, Feng-Bin Wang) JDE 259(2015)no. 10, p. 5353-5378PDF
  4. Algal competition in a water column with excessive dioxide in the atmosphere .(with Hua Nie and J.P.Grover) J.Math. Biology(2016) vol21,No.2 p.437-446 PDF
  5. Coexistence solutions of a competitive model with two species in a water column (with Hua Nie and Jianhua Wu), in DCDS-B 20(2015)no.8, 26941-2714PDF
  6. A reaction-diffusion-advection model of harmful algae growth with toxin degradation (with Feng-Bin Wang and Xiaoqiang Zhao), in JDE, 259(2015) p.3178-3201 PDF
  7. " Theory of a microfluidic serial dilution bioreactor for growth of planktonic and biofilm population" (with Ya-Tang Yang) J. Math. Biology 72 (2016) ,1401-1427. PDF
  8. "A pivotal eigenvalue problem in river ecology" (with J. Lopez-Gomez,Lingfen Mei,Feng-Bin Wang), JDE 29(2015)2280-2316. PDF
  9. "Analysis of three species Lotka-Volterra food web models with omnivory" (with Shigui Ruan and Ting-Hui Yang),J.Mathematical Analysis and Applications,426 (2015) 659-687. PDF
  10. "A NONLOCAL PROBLEM FROM CONSERVATION BIOLOGY" ( with J. LO_ PEZ-GO_MEZ, L. MEI, AND M. MOLINA-MEYER), SIAM Journal of Mathematical Analysis, 46-6(2014) p.4035-4059. PDF
  11. "MULTIPLE STEADY-STATES IN PHYTOPLANKTON POPULATION INDUCED BY PHOTOINHIBITION" ( with YIHONG DU, YUAN LOU), JDE.258(201) 2408-2434 PDF
  12. "Dynamics of two phytoplankton Species Competing for light and nutrient with internal storage." (with C.J. Lin),DCDS-S 7(2014) no.6. p.1259-1285.PDF
  13. "On the Dynamics of Two-consumers-one-resource Competing Systems with Beddington-DeAngelis Functional Response'' (with Shigui Ruan, and Ting-Hui Yang),DCDS-B, 18(2013) NO.9, pp2331-2353. PDF
  14. "FURTHER STUDIES OF A REACTION-DIFFUSION SYSTEM FOR AN UNSTIRRED CHEMOSTAT WITH INTERNAL STORAGE" (with Junping Shi and Feng-Bin Wang) DCDS-B,19(2014),no.10 (December).PDF
  15. "Global Dynamics of Zooplankton and Harmful Algae in Flowing Habitats'' (with Feng-Bin Wang, Xiao-Qiang Zhao), JDE 255(2013), pp 265-297.  PDF 
  16. " Dynamics of Phytoplankton Communities Under Photoinhibition'' (with Chiu-Ju Lin , Chih-Hao Hsieh, Kohei Yoshiyama), Bulletin of Math Biology 75(2013) No.7, p.1207-1232. PDF 
  17. "Subfunctionalization reduces the fitness cost of gene duplication in humans by buffering dosage imbalances " (with Ariel Fern_ndez, Yun-Huei Tzeng)  Genomics 2011, 12:604,  PDF 
  18. "A Refuge-mediated Apparent Competition Model" (with Lih-Ing Wu Roeger), Canadian Applied Math. Quaterly 19(2013) No. 3,  pp 219-234.  PDF
  19. "ReactioníVdiffusion equations of two species competing for two complementary resources with internal storage"  (with Jifa Jiang and Feng-Bin Wang)  J. Diff. Equat. Vol 251(2011) pp 918-940  PDF
  20. "Competition between microorganisms for a single limiting resource with cell quota structure and spatial variation  (with James P. Grover and Feng-Bin Wang) J. Math. Biol 64(2012), No. 5, pp 713-743..  PDF

21.  "Dynamics of a Periodically Pulsed Bio-Reactor Model With a Hydraulic Storage Zone" (with Feng-Bin Wang and Xiaoqiang Zhao) J Dyn Diff Equat 23(2011), No. 4, pp 817-842.  PDF 

22.  "A Lotka-Volterra Competition model with season succession" (with Xiaoqiang Zhao)  J. Math. Biology (2012), 64,p.109-130 PDF 

23.  "Synchronized reproduction promotes species coexistence through reproductive facilitation"(with Yu-Yun Chen), J.Theoretical Biology 274(2011), pp 136-144 PDF 

  1. "Single phytoplankton species growth with light and advection in a water column" (with Yuan Lou),  SIAM J. Appli. Math., Vol 70,(2010) No.8, pp 2942-2974  PDF

25.  "on a system of reaction-diffusion equations arising from competition with internal storage in an unstirred chemostat" (with Jifa Jiang, Feng-Bin Wang) , JDE 248 (2010), pp 2470-2496 PDF

26.  "On a nonlocal reaction-diffusion problem arising from the modeling phytoplankton growth" (with Yihong Du), SIAM J. Math. Analysis 42 (2010), pp 1305-1333 PDF

27.  "On a mathematical modelarising from cpmpetition of phytoplankton species for a single nutrient with internal storage: Steady state analysis." (with  Feng-Bin Wang) , Commun. Pure Appl. Anal. 10 (2011) ,no.5,1479-1501 PDF

28.  Competition and coexistence in flowing habitats with a hydraulic storage zone" (with James P. Grover, Feng-Bin Wang) , Mathematical Biosciences, Vol. 222 (2009), pp. 42-52 PDF

29.  "Heteroclinic cycles in the chemostat models and the winnerless competition principle" (with Lih-Ing W. Roeger) , JMAA, (2009), PDF

30.  "Relaxation oscillation profile of limit cycle in predator-prey system" (with Junping Shi) , DCDS-B, Vol. 11 (2009), No. 4, pp. 893-911 PDF

31.  " Analysis of a Model of Two Parallel Food Chains" (withChristopher A. Klausmeier, Chiu-Ju Lin) , DCDS-B, Vol. 9 (2009), No. 2,pp. 337-359 PDF

32.  "Mathematical Analysi of Two Microbial Species Competing for Two Complementary Resources with Internal Storages and Different Removal, DilutionRates" (with Fern-Bin Wang) , Bulletin of the Institute of Mathematics Academia Sinica, Vol. 3 (2008), No. 4, pp. 487-508 PDF

33.  " Non-periodicity of chemostats: a multi-dimensional negative Bendixson Dulac criterion" (with Bernold Fiedler) , J. Math. Biology, Vol. 59(2009), No. 2, pp. 233-253 PDF

34.  "Concentration Phenomena in a Nonlocal Quasilinear Problem Modelling Phytoplankton I: Existence" (with YIHONG DU) SIAM Journal of Mathematical Analysis, Vol 40, p1419-1440 (2008) PDF

35.  "Concentration Phenomena in a Nonlocal Quasilinear Problem Modelling Phytoplankton II: Limiting Profile" (with YIHONG DU) SIAM Journal of Mathematical Analysis, Vol 40, p1441-1470 (2008) PDF

36.  "Competitive Exclusion of Microbial Species for a Single-Nutrient with Internal Storage" (with TING-HAO HSU) SIAM. J. Appl. Math, Vol 68,(2008) No. 6, p1600-1617 PDF

37.  "Spreading Speeds and Traveling Waves for Non-Monotone Integrodifference Equations"(with XIAO-QIANG ZHAO) SIAM J. Math. Analysis, , Vol 40,(2008) No. 2, p776-789 PDF

38.  "Global Dynamics of a Predator-Prey Model with HASSELL-VARLEY Type Functional Response" (with Tzy-Wei Hwang, Yang Kuang) Discrete and Continuous Dynamical System, Series B, Vol 10,(2008) No. 4, p857-871 PDF

39.  "On the Role of Asymptomatic Infection in Transmission Dynamics of Infectious Diseases"(with Ying-Hen Hsieh)Bulletin of Mathematical Biology (2008) 70: 134íV155 PDF

  1. "Impact of quarantine on the 2003 SARS outbreak: A retrospective modeling study" (with Ying-Hen Hsieh et), Journal of Theoretical Biology, 244, (2007), 729-736 PDF

41.  "The final size of a SARS epidemic model without quarqntine" (with Lih-Ing W. Roeger), J. Math. Anal. Appl., 333, (2007), 557-566 PDF

42.  "Modeling intervention measures and severity-dependent public response during severe acute respiratory Syndrome Otubreak" (with Ying-Hen Hsieh), SIAM J. Appl. Math., vol 66, No.2, (2006), 627-647   PDF

43.  "Constructing Lyapunov Functions for Mathematical Models in Population Biology", Taiwanese Journal of Math., vol 9, No.2, (2005), 151-173.   PDF

44.  "A Discrete-Delayed model with Plasmid-Bearing, Plasmid-Free Competition in a Chemostat" (with Cheng-Che Li), DCDS, vol 5, No.3, (2005), 699-718.    PDF

45.  "A diffusive predator-prey model in heterogeneous environment", (with Yihong Du), JDE 203(2004) 331-364.    PDF

46.  "A survey of Mathematical Models of Competition with on inhibitor", (with Paul Waltman). Math. Biosci. 187(2004) 53-91   PDF

47.  "The Severe Acute Respiratory Syndrome Outbreak in Taiwan: Lesson to be learn" (with Ying-Hen Hsieh, Cathy W. S. Chen) Emerging Infectious Diseases (2004) vol 10,No.2, 201-206   PDF

48.  "Heteroclinic Foliation, Global Oscillations for the Nicholson-Bailey Model and Delay of Stability Loss" (with Ming-Chia Li, Weishi Liu, Mikhail Malkin) Discrete and c ontinuous Dynamical Systems ,vol 9,No. 6,(2003),1465-1492   PDF

49.  "A Ratio-Depentent Food Chain Model and its Application to Biological control" (with T.W.Huang ,Y.Kuang) Math.Bios.181(2003)55-83   PDF

50.  "Plasmid-bearing ,plasmid-free organisms Competing for two complementary nutrients in a chemostat" (with Yun-Huei Tzeng) Math Bios 179 (2002)183-206   PDF

51.  "A model of the effect of anti-competitor toxins on plasmid-bearing ,plasmid-free competition" (P.Waltman) Taiwanese J.Math 6(1)(2002)135-155   PDF

52.  "Rich dynamics of a ratio-dependent one prey two predator model" (with T.W.Hwang and Y.Kuang) J.Math.Biology 43 (2001), 377-396   PDF

53.  "Chaotic behavior of three competing species of May-Leonard model under small periodic perturbation ", (with V, Afraimovich, Huey-Er Lin ), International J. of Bifurcation and Chaos, Vol. 11, No. 2 (2001) 435-447.   PDF

54.  "Global Analysis of the Michaelis-Menten type ratio-dependence predator-prey system", (with T. W. Hwang and Y. Kuang), J. Math. Biol.(2001), 42, 489-506.   PDF

55.  "Stability analysis for a class of diffusive coupled system with applications to population biology ", (with Ruey-Tarng Gong), Canadian Applied Math. Quarterly (2000) Vol. 8, P. 79-96.   PDF

56.  "Competition in the presence of a lethal external inhibitor",(with Yen-Sheng Li and Paul Waltman), Math. Bioscience 167(2000)177-199.   PDF

57.  "Hopf Bifurcation Analysis for a Predator-Prey system of Holling and Leslie type", (with T.W. Hwang), {Taiwanese Journal of Mathematics}, (1999) Vol. 3, No. 1, p.35-53.   PDF

58.  "Extinction of top predator in a three level food chain model", (with C.H. Chiu), {J. Math. Biology}, (1998) vol. 37, P.372-380.   PDF

59.  "Competition in the chemostat when one competitor produces a toxin", (with P. Waltman) {Japan SIAM J. Applied Mathematics} (1998), Vol. 15, No. 3 p.471-490.   PDF

60.  "Uniqueness of limit cycles for a Predator--Prey system of Holling and Leslie type", (with T.W. Hwang), {Quarterly Canadian Applied Mathematics}, (1998) Vol. 6, No. 2, p.91-117. PDF

61.  "Competition between Plasmid--Bearing and Plasmid--Free organisms in selective media", (with P. Waltman), {\mbs Chemical Engineering Science}, Vol. 52 (1997), 23-35.   PDF

62.  "On the asymmetric May-Leonard model of three competing species",(with Chia-Wei Chi and Lih-Ing Wu), {SIAM J. of Applied Math.}, Vol. 58, No. 1, p.211--226 (1998).   PDF

63.  "Competitive exclusion and coexistence for competitive system on ordered Banach space", (with H.L. Smith and P. Waltman), {AMS Transaction}, Vol. 348 (1996), 4083-4094.   PDF

64.  "Competition between Plasmid--Bearing and Plasmid--Free organisms in a chemostat with inhibitor", (with T.K. Luo and P. Waltman), {J. of Math. Biology}, Vol. 34 (1995), 225-238.   PDF

65.  "Global analysis of a model of Plasmid--Bearing, Plasmid--Free competition in a chemostat with inhibitions", (with T.K. Luo), {J. of Math. Biology}, Vol. 34 (1995), 41-76. PDF

66.  "Global stability for a class of Predator--Prey systems", (with Tzy--Wei Huang), {SIAM J. Appl. Math.}, Vol. 55, No. 3 (1995), 763-783.  PDF

67.  "Global analysis of a model of Plasmid--Bearing, Plasmid--Free competition in a chemostat", (with P. Waltman and G. Wolkowicz), {Journal of Mathematical Biology} 32 (1994), 731-742.  PDF

68.  "Dynamics of competition in the unstirred chemostat", (with H. Smith and P. Waltman), {Canadian Appl. Math. Quarterly} (1994), 461-483.  PDF

69.  "A remark on the global asymptotic stability of A dynamical system modeling two species competition", (with P.E. Waltman and S. Ellermeyer), {Hiroshima Mathematical Journal}, Vol 24. No. 2 (1994) 435-445. PDF

70.  "On a system of Reaction--Diffusion equations arising from competition in an unstirred chemostat", (with P.E. Waltman), {SIAM J. Appl. Math.}, Vol. 53, No. 4, (1993), 1026-1044. PDF

71.  "Analysis of a model of two competitors in a chemostat with an external inhibitor", (with P.E. Waltman), {SIAM J. Applied Math.}, Vol. 52, No. 2, (1992), 528-540.  PDF

72.  "A mathematical model of chemostat with periodic washout rate", (with Butler, Waltman), {SIAM, J. Appl. math.}, Vol. 45, No. 3, (1985), 435-449.  PDF

73.  "Steady state of a system of P.D.E. modeling microbial ecology", {SIAM J. Math. Analysis}, Vol. 14 (1983), 1130-1138.  PDF

74.  "Coexistence of competing predator in a chemostat", (with G.J. Butler and P.E. Waltman), {J. Math. Biology}, 17 (1983), 133-151. PDF

75.  "A remark on the period of periodic solutions in the Lotka--Volterra system", {J. Math. Analysis and Application}, Vol. 95, No. 2, (1983), 428-436. PDF

76.  "Predator--Mediated coexistence and extinction", {Math. Bios.}, 54 (1981), 231-248. PDF

77.  "Exploitative competition of two Micro--Organisms for two complementary nutrients in a continuous culture", (with Cheng, Hubbell), {SIAM J. App. Math.}, (1981), 422-444.  PDF

78.  "Some results on global stability of a Predator--Prey system", (with S.S. Lin and Cheng), {J. Math., Biology}, 12 (1981), 115-126.PDF

79.  "On a resource based ecological competition model with interference", {J. Math. Biology}, 12 (1981), 45-52.PDF

80.  "A competition model for a seasonally flluctuating nutrient", {J. Math. Biology}, 9 (1980), 115-132. PDF

81.  "Two predators competing for two prey species_G An analysis of MacArthur's model", (with Hubbell), {Math. Biocience} 43 (1979), 143-171.  PDF

82.  "Theoretical and experimental investigation of microbial competition in continuous culture", (with Waltman, Hubbell), {Proceeding of Conference in Biomathematics at Southern Illinois University}, edited by Burton, (1978) 107-152. PDF

83.  "Competing predator", (with Waltman, Hubbell), {SIAM J. Appl math.}, Vol. 135, No. 4 (1978), 617-625.PDF

84.  "A contribution to the theory of competing predators", (with Waltman, Hubbell), Ecological Monograph, 38 (1978), 337-349.  PDF

85.  "Limiting behavior for competing species", SIAM, J. Appl. Math., Vol. 34, No. 4 (1978), 760-763.  PDF

86.  "On global stability of a Predator--Prey system", Math. Bioscience, 39 (1978), 1-10. PDF

87.  "The application of the Poincare--Transform to the Lotka--Volterra model", J. Math. Biology, 6 (1978), 67-73. PDF

88.  "A mathematical theory for Single--Nutrient competition in continuous culture of Micro--Organisms", (with Waltman, Hubbell), SIAM J. Appl. Math. Vol. 32, No. 2 (1977), 366-382.  PDF

    II.         Chaotic Vibrating Strings

1.     "THE SPECTRUM OF CHAOTIC TIME SERIES (II): WAVELET ANALYSIS" (with GOONG CHEN, YU HUANG, and MARCO A. ROQUE-SOL) International Journal of Bifurcation and Chaos, Vol. 21, No. 5 (2011) 1457íV1467   PDF

2.     "THE SPECTRUM OF CHAOTIC TIME SERIES (I): FOURIER ANALYSIS" (with GOONG CHEN, YU HUANG, and MARCO A. ROQUE-SOL) International Journal of Bifurcation and Chaos, Vol. 21, No. 5 (2011) 1439íV145   PDF

3.     "Chaotic Vibration of the Wave Wquation with Nonlinear Feedback Boundary Control: Progress and Open Problems" (with Goong Chen and Jianxin Zhou) Chapter 2, Chaos Control, Vol I ,Chaos and Bifurcation Control: Theory and Applications,Edited by Guanrong Chen, Lecture Note in Control and Information Science, Springer Verlag (2003)   PDF

4.     "Analyzing Displacement Term's Memory Effect in a van der Pol Type Boundary Condition to Prove Chaotic Vibration of the Wave Equation" (with Goong Chen & Tingwen Huang)International J. of Bifurcation and Chaos vol 12 ,No5 (2002) 965-982   PDF

5.     "Nonisotropic spatiotemporal chaotic vibration on the Wave equation due to mixing energy transport and a Van der Pol boundary condition" (with Goong Chen & Jianxin Zhou)International J. of Bifurcation and Chaos vol 12,No3 (2002) 535-559   PDF

6.     "Chaotic Vibration of the Wave Equation by Nonlinear Feedback Boundary Control", Chapter 7, p.131-154, {Controlling Chaos and Bifurcation in Engineering}, CRC Press, edited by Guangrong Chen (1999). PDF

7.     "Snapback Repellers as a Cause of Chaotic Vibration of the Wave Equation with a Van Der Pol boundary condition and energy injection at the middle of the span", (with G. Chen and J. Zhou), {J. of Math. Physics} (1998) Vol. 39, No. 12, p.6459-6489.   PDF

8.     "Chaotic vibration of the one-dimensional wave equation due to a self-excitation boundary condition, Part III_G Natural hysteresis memory effects", (with G. Chen and J. Zhou), {International Journal of bifurcation and Chaos}, Vol. 8, No. 3 (1998) p.447-470.   PDF

9.     "Chaotic vibration the one-dimensional wave equation due to a self-excitation boundary condition PartII_G Energy Pumping, Period doubling and homoclinic orbits", (with G. Chen and J. Zhou), {International Journal of Bifurcation and Chaos}, Vol. 8, No. 3 (1998) p.423-445.   PDF

10.  "Chaotic vibrations of the One-Dimensional wave equation due to a Self-Excitation boundary condition, Part I_Gcontrolled hysteresis", (with G. Chen and J. Zhou), { AMS Transaction}, (1998) Vol. 350, No. 11, p.4265-4311.   PDF

11.  "Linear superposition of chaotic and orderly vibrations on two serially connected string with a van der Pol Joint", (with G. Chen and J. Zhou), {International J. of Bifurcation and chaos}, Vol. 6 (1996), 1509-1527. PDF

  III.         Mechanics and Gas Dynamics

1.     Classification of potential flows under renormalization group transforms (with Bernold Fiedler and Hsui-Hau Lin) ,Discrete Continuous Dynamical System Series B, 21(2016) no.2, 437-446.  PDF

2.     Hierarchy of relevant couplings in perturbative renormalization group transformations" (with Hong-Yan Shih, Wen-Ming Huang, and Hsiu-Hau Lin1) Physical review B 81 ([1] 2010)  PDF

3.     "Mathematical Analysis of a Bohr Atom Model" (with Goong Chen et) , to appear in Journal of Mathematical Physics . PDF

4.     "A Qualitative Study on the Damped Duffing Equation and Applications" (with Z. Feng, G. Chen), Discrete and Continuous Dynamical Systems Series B, vol. 6, No.5 (2006), 1097-1112.   PDF

5.     "On the singular behavior of v''(x)+x sin v(x)=0", (with K.S. Cheng, S.F. Hwang), Journal of Mathematical Analysis and Applications}, Vol. 163, No. 1 (1992), 20-37. PDF

6.     "Nonlinear singular Sturm--Liouville problem and application to transonic flow through a nozzle", (with Tai-Ping Liu), {\mbs Communication in Pure and Applied Mathematics}, Vol. XLIII (1990), 31-61. PDF

7.     "Uniqueness property of large deformation of a heavy cantilever",{Bulltin of the Institute of Mathematics Academia Sinica}, Vol. 17, No. 3 (1989), 193-204.  PDF

8.     "On the asymptotic behavior of solutions of v''(x) + x sin v(x)=0", (with W.M. Ni), {Bulltin of the Institute of Mathematics Academia Sinica}, Vol. 16, No. 2 (1988), 109-114. 

9.     "Anlaysis of large deformation of heavy cantilever", (with S.F. Hwang), {SIAM J. Math. Analysis}, Vol. 19, No. 4 (1988), 854-866.  PDF