Yi Li, Ph.D.

yi li.jpeg

Professor, Department of Mathematics and Statistics

Dean, College of Science and Mathematics

Wright State University

134 Oelman Hall
College of Science and Mathematics
Wright State University
3640 Colonel Glenn Highway
Dayton, OH 45435-0001

Phone: (937) 775-2611
Fax: (937) 775-3068

Email: yi.li@wright.edu

Biography

Dr. Li came to Wright State from the University of Iowa (UI) in 2011, where he had served as the mathematics department chair since 2007. Prior to this, after earning a Ph.D. in 1988, he spent two years as a L.E. Dickson Instructor at the University of Chicago. Following this, he taught at the University of Rochester in Rochester, N.Y. before going to UI in 1996. Before serving as department chair at UI, Li served as the UI director of the Applied Mathematical and Computational Sciences program, associate chair/director of Graduate Studies and acting director of Undergraduate Studies. 

Dr. Li studies nonlinear problems and their applications in physics, geometry, and biomedical research. He has worked on new ways to study the conformal scalar curvature equations in differential geometry and Matukuma's equation in astrophysics. While working on bioluminescence tomography, Li with G. Wang invented the computational optical biopsy modality. Li has also worked in the area of traveling fronts, a fundamental problem related in population dynamics, genetics, and flame propagation. In particular, he solved an open problem left by Berestycki and Nirenberg on the uniqueness and asymptotic behavior of such solutions for a semi-degenerated nonlinearity. He and his co-authors also settled another long-standing open problem on the stability of marginal speed traveling fronts for this semi-degenerated nonlinearity. His work has been published in more than 70 peer-reviewed publications, and supported by NSF and NIH. 

Publications

If you would like to receive a copy of any of the following publications, please click on the Request a Copy link for the specific title you are interested in.

Li, Yi; Peng, Shuangjie Multiple solutions for an elliptic problem related to vortex pairs. Journal of Differential Equations 250 (April 15, 2011) no. 8, 3448--3472. Request a Copy

Dai Donghai; Beck Brandon; Wang Xiaofang; et al. Quantitative Interpretation of a Genetic Model of Carcinogenesis Using Computer Simulations. PLOS ONE 6 (March 8, 2011), no. 3, Article Number: e16859 Request a Copy

Batt, J.; Li, Y. The positive solutions of the Matukuma equation and the problem of finite radius and finite mass. Arch. Rational Mech. Anal. 198 (2010) no. 2, 613--675. Request a Copy

Korman, P.; Li, Y. Computing the location and the direction of bifurcation for sign changing solutions. Differential Equations and Applications 2 (2010), no. 1, 1--13. Request a Copy

Li, Y.; Zhao, C.-S. On the structure of solutions to a class of quasilinear elliptic Neumann problems. II, Journal of Calculus of Variations and Partial Differential Equations 37 (2010), no. 1-2, 237--258. Request a Copy

Li, Y.; Zhou, S.-Q. Some remarks on the positive solution for a semilinear Shrödinger-Poisson-Slater system in Rn. Advances in Mathematics 39 (2010) no. 3, 303--312. Request a Copy

Rivera, J.; Li, Y. Traveling wave solutions for a nonlocal reaction-diffusion model of Influenza A drift. Discrete and Continuous Dynamical Systems B 13 (2010), no. 1, 157--174. Request a Copy

Hou, X.-J.; Li, Y.; Meyer, K. Traveling wave solutions of the one dimensional diffusion-reaction equation. Discrete and Continuous Dynamical Systems 26 (2010), no. 1, 265--290. Request a Copy

Deng, Y.-B. ; Li, Y. Regularity of the solutions for nonlinear biharmonic equations in Rn. Acta Math. Sci. 29B (2009), 1469--1480. Request a Copy

Deng, Y.-B.; Li, Y.; Yang, F. A note on the positive solutions of an inhomogeneous elliptic equation on Rn. J. Differential Equations 240 (2009), 670--680. Request a Copy

Li, T.; Li Y.; Hethcote, Herbert Periodic traveling wave solutions in epidemiological models. J. Math. & Comp. Modeling 49 (2009), 393--401. Request a Copy

Deng, Yinbin; Li, Yi; Yang, Fen A note on the positive solutions of an inhomogeneous elliptic equation on Rn. J. Differential Equations 240 (2009), 670--680. Request a Copy

Lai, B.-S.; Li, Y. On the semistability of the minimal positive steady state for a nonhomogeneous semilinear Cauchy problem. Mathematical Research Letters 15 (2008), no. 5, 923--939. Request a Copy

Li, Yi; Liu, Zhaoli ; Chunshan, Zhao Nodal solutions of a perturbed elliptic problem. Topological Methods in Nonlinear Analysis 32 (2008), no. 1, 49--68. Request a Copy

Chen, Hongbin; Li, Yi Bifurcation and stability of periodic solutions of Duffing equations. Nonlinearity 21 (2008), 2485--2503. Request a Copy

Baishun, Lai; Li, Yi On the semistability of the minimal positive steady state for a nonhomogeneous semilinear Cauchy problem. Mathematical Research Letters 15 (2008), no. 5, 923--939. Request a Copy

He, Y. N.; Li, Y. Asymptotic behavior of linearized viscoelastic flow problem. Discrete and Continuous Dynamical Systems B 10(4) (2008), 843--856. Request a Copy

Deng, Yinbin; Guo, Yujin; Li, Yi Existence and decay properties of positive solutions for an inhomogeneous semilinear elliptic equation. Proceedings of the Royal Society of Edinburgh Sect. A 138 (2008), no. 2, 301--322. Request a Copy

Li, Yi; Wu, Y.-P. Stability of travelling waves with noncritical speeds for double degenerate Fisher-type equations. Discrete and Continuous Dynamical Systems B 10 (2008), no. 1, 149--170. Request a Copy

Leung, A.; Hou, X.-J.; Li, Y. Exclusive traveling waves for competitive reaction-diffusion systems and their stabilities. Journal of Mathematical Analysis and Applications 338 (2) (2008), 902--924. Request a Copy

Korman, P.; Li, Y.; Ouyang, T.-C. Verification of bifurcation diagrams for polynomial-like equations. Journal of Computational and Applied Mathematics 2 (2008), 187--193. Request a Copy

Deng, Yinbin; Li, Yi Exponential decay for nonlinear biharmonic equations. Communications in Contemporary Mathematics 9 (2007), no. 5, 753--768. Request a Copy

Li, Yi; Zhao, Chunshan Locating the peaks of least-energy solutions to a quasilinear elliptic Neumann problem. Journal of Mathematical Analysis and Applications 336 (2007), no. 2, 1368--1383. Request a Copy

Chen, Hongbin; Li, Yi Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities. Proceedings of AMS 135 (2007), no. 12, 3925--3932. Request a Copy

Chen, Hongbin; Li, Yi Existence, uniqueness, and stability of periodic solutions of an equation of Duffing-type. Discrete and Continuous Dynamical Systems A 18 (2007), no. 4, 793--807. Request a Copy

Rivera, Joaquin; Li, Yi On the exact multiplicity of solutions for boundary-value problems via computing the direction of bifurcations. Proceeding of the MSU-UAB Conference, Electron. J. Diff. Eqns 15 (2007), 239--249. Request a Copy

Hou, Xiaojie; Korman, Philip; Li, Yi On the direction of pitchfork bifurcation. Proceeding of the MSU-UAB Conference, Electron. J. Diff. Eqns 15 (2007), 153--158. Request a Copy

Chen, Hongbin; Li, Yi Rate of decay of stable periodic solutions of Duffing equations. J. Differential Equations 236 (2007), no. 2, 493--503. Request a Copy

Li, Yi; Zhao, Chunshan On the shape of least-energy solutions for a class of quasilinear elliptic Neumann problems. IMA Journal of Applied Mathematics 72 (2007), no. 2, 113--139. Request a Copy

Coskun, Huseyin; Li, Yi; Mackey, Michael A. Ameboid cell motility: a model and inverse problem, with an application to live cell imaging data. Journal of Theoretical Biology 244 (2007), no. 2, 169--179. Request a Copy

Wang, Wendi; Li, Yi; Hethcote, Herbert W. Bifurcations in a host-parasite model with nonlinear incidence. International Journal of Bifurcation and Chaos 16 (2006), no. 11, 3291--3307. Request a Copy

Deng, Yinbin; Li, Yi Branches of solutions to semilinear biharmonic equations on Rn. Proceedings of the Royal Society of Edinburgh Sect. A 136 (2006), no. 4, 733--758. Request a Copy

Galstyan, A; Korman, Philip; Li, Yi On the oscillations of the solution curve for a class of semilinear equations. Journal of Mathematical Analysis and Applications 321 (2006), no. 2, 576--588. Request a Copy

Li, Yi; Zhao, Chunshan Existence, uniqueness and decay properties of strong solutions to an evolutionary system of MHD type in R3. J. Dynam. Differential Equations 18 (2006), no. 2, 393--426. Request a Copy

Wang, G.; Qian, X.; Cong, W.; Shen, H.; Li, Y.; Han, W. M.; Durairaj, K.; Jiang, M.; Zhou, T.; Cheng, J. T.; Tian, J.; Lv, Y. J.; Li, H.; Luo, J. Recent development in bioluminescence tomography. Current Medical Imaging Reviews, 2 (4) (2006), 453--457. Request a Copy

Hou, Xiaojie; Li, Yi Local stability of traveling wave solutions of nonlinear reaction diffusion equations. Discrete and Continuous Dynamical Systems A, 15 (2006), 681--701. Request a Copy

Deng, Yinbin; Li, Yi; Yang, Fen On the stability of the positive radical steady states for a nonhomogeneous semilinear Cauchy problem. J. Differential Equations 228 (2006), 507--529. Request a Copy

Hethcote H. W.; Wang, Wendi; Li, Yi Species coexistence and periodicity in host-host-pathogen models. Journal of Mathematical Biology v51 #6 (2005), 629--660. Request a Copy

Korman, Philip; Li, Yi; Ouyang, Tiancheng Computing the location and the direction of bifurcation. Mathematical Research Letters (2005), no. 5-6, 933--944. Request a Copy

Li, Yi; Jiang, Ming; Wang, Ge Computational optical biopsy. BioMedical Engineering OnLine (2005), 1--7. Request a Copy

Li, Yi; Zhao, Chunshan A note on exponential decay properties of ground states for quasilinear elliptic equations. Proceedings of AMS 133 (2005), 2005--2012. Request a Copy

Li, Yi; Zhao, Chunshan Global existence of solutions to a cross-diffusion system in higher dimensional domains. Discrete and Continuous Dynamical Systems 12 (2005), 185--192. Request a Copy

Li, Yi; Zhao, Chunshan On the structure of solutions to a class of quasilinear elliptic Neumann problems. Journal of Differential Equations 212 (2005), 208--233. Request a Copy

Wang, Ge; Li, Yi; Jiang, Ming Uniqueness theorems in bioluminescence tomography. Medical Physics 31 (2004), 2289--2299. Request a Copy

Chen, Hongbin; Li, Yi Exact multiplicity for periodic solutions of a first-order differential equation. Journal of Mathematical Analysis and Applications, 292/2 (2004), 415--422. Request a Copy

Chen, Hongbin; Li, Yi; Hou, Xiaojie Exact multiplicity for periodic solutions of Duffing type. Nonlinear Analysis. Theory, Methods & Applications 55 (2003), no. 1-2, 115--124. Request a Copy

Deng, Yinbin; Li, Yi; Liu, Yi On the stability of the positive radial steady states for a semilinear Cauchy problem. Nonlinear Analysis. Theory, Methods & Applications 54 (2003), no. 2, 291--318. Request a Copy

Li, Yi; Qi, Yuanwei The global dynamics of isothermal chemical systems with critical nonlinearity. Nonlinearity 16 (2003), 1057--1074. Request a Copy

Korman, Philip; Li, Yi; Ouyang, Tiancheng Perturbation of global solution curves for semilinear problems. Advanced Nonlinear Studies 3 (2003), no. 2, 289--299. Request a Copy

Deng, Yinbin; Li, Yi; Zhao, Xuejin Multiple solutions for an inhomogeneous semilinear elliptic equation in Rn. Acta Math. Sci. Ser. B Engl. Ed. 23 (2003), no. 1, 1--15. 35J60 (35J20) Request a Copy

Deng, Yinbin; Li, Yi On the existence of multiple positive solutions for a semilinear problem in exterior domains. J. Differential Equations 181 (2002), no. 1, 197-229. 35J60 (35B05 35J25) Request a Copy

Liu, Yi; Li, Yi; Deng, Yinbin Separation property of solutions for a semilinear elliptic equation. J. Differential Equations 163 (2000), no. 2, 381--406. (Reviewer: Alan V. Lair) 35J60 (35B05 35B40) Request a Copy

Deng, Yinbin; Li, Yi; Zhao, Xuejin Multiple solutions and bifurcation of nonhomogeneous semilinear elliptic equations in Rn. Progress in nonlinear analysis (Tianjin, 1999), 81--102, Nankai Ser. Pure Appl. Math. Theoret. Phys., 6, World Sci. Publishing, River Edge, NJ, 2000. 35J60 (35J20 47J15 58E07) Request a Copy

Korman, Philip; Li, Yi Infinitely many solutions at a resonance. Proceedings of the Conference on Nonlinear Differential Equations (Coral Gables, FL, 1999), 105--111 (electronic), Electron. J. Differ. Equ. Conf., 5, Southwest Texas State Univ., San Marcos, TX, 2000. 34B15 (34C23) Request a Copy

Liu, Yi; Li, Yi; Deng, Yinbin Stability of a semilinear Cauchy problem. Partial differential equations and their applications (Wuhan, 1999), 180--199, World Sci. Publishing, River Edge, NJ, 1999. 35K55 (34A12 35B05 35B35 35C20) Request a Copy

Hethcote, H. W.; Li, Yi; Jing, Zhujun Hopf bifurcation in models for pertussis epidemiology. Math. Comput. Modelling 30 (1999), no. 11-12, 29--45. 92D30 (34C23 34C60 37N25) Request a Copy

Korman, Philip; Li, Yi On the exactness of an S-shaped bifurcation curve. Proc. Amer. Math. Soc. 127 (1999), no. 4, 1011--1020. 34B15 (34C23) Request a Copy

Korman, Philip; Li, Yi Generalized averages for solutions of two-point Dirichlet problems. J. Math. Anal. Appl. 239 (1999), no. 2, 478--484. 34B18 Request a Copy

Cac, Nguyen Phuong; Gatica, Juan A.; Li, Yi Positive solutions to semilinear problems with coefficient that changes sign. Nonlinear Anal. 37 (1999), no. 4, Ser. A: Theory Methods, 501--510. 35J65 (35B05) Request a Copy

Wang, G.; Li, Y. Axiomatic approach for quantification of image resolution. IEEE Signal Processing Letters 6:257--258, 1999. Request a Copy

Li, Yi Exact multiplicity of positive solutions of some elliptic problems. Bifurcation theory & its numerical analysis (Xi'an, 1998), 133--144, Springer, Singapore, 1999. 35J65 (34B15 34B18 35B05 47J15 58E05) Request a Copy

Cranston, Michael; Li, Yi Eigenfunction and harmonic function estimates in domains with horns and cusps. Comm. Partial Differential Equations 22 (1997), no. 11-12, 1805--1836. 35J05 (35B45 35P15) Request a Copy

Bebernes, Jerrold W.; Li, Comgming; Li, Yi Travelling fronts in cylinders and their stability. Rocky Mountain J. Math. 27 (1997), no. 1, 123--150. 35K57 (35B40) Request a Copy

Korman, Philip; Li, Yi; Ouyang, Tiancheng An exact multiplicity result for a class of semilinear equations. Comm. Partial Differential Equations 22 (1997), no. 3-4, 661--684. 35J60 (34B15 35B32 47H15 47N20) Request a Copy

Deng, Yinbing; Li, Yi Existence of multiple positive solutions for a semilinear elliptic equation. Adv. Differential Equations 2 (1997), no. 3, 361--382. 35J60 (35B05 35B32) Request a Copy

Korman, Philip; Lazer, Alan C.; Li, Yi On homoclinic and heteroclinic orbits for Hamiltonian systems. Differential Integral Equations 10 (1997), no. 2, 357--368. 34C37 (58E05 58F05 70H05) Request a Copy

Deng, Yinbin; Li, Yi Existence and bifurcation of the positive solutions for a semilinear equation with critical exponent. J. Differential Equations 130 (1996), no. 1, 179--200. 35J60 (35B32) Request a Copy

Korman, Philip; Li, Yi; Ouyang, Tiancheng Exact multiplicity results for boundary value problems with nonlinearities generalising cubic. Proc. Roy. Soc. Edinburgh Sect. A 126 (1996), no. 3, 599--616. 34B15 Request a Copy

Dawson, D.; Li, Y.; Mueller, C. The support of measure-valued branching processes in a random environment. Ann. Probab. 23 (1995), no. 4, 1692--1718.60J80 Request a Copy

Dawson, Donald A.; Fleischmann, Klaus; Li, Yi; Mueller, Carl Singularity of super-Brownian local time at a point catalyst. Ann. Probab. 23 (1995), no. 1, 37--55. 60J80 (60G57 60J65) Request a Copy

Li, Yi; Santanilla, Jairo Existence and nonexistence of positive singular solutions for semilinear elliptic problems with applications in astrophysics. Differential Integral Equations 8 (1995), no. 6, 1369--1383. 35J60 (35B05 85A15) Request a Copy

Gage, Michael E.; Li, Yi Evolving plane curves by curvature in relative geometries. II. Duke Math. J. 75 (1994), no. 1, 79--98. 53A04 (58E10) Request a Copy

Li, Yi; Ni, Wei-Ming Radial symmetry of positive solutions of nonlinear elliptic equations in Rn. Comm. Partial Differential Equations 18 (1993), no. 5-6, 1043--1054. 35B05 (35J60) Request a Copy

Kaper, Hans G.; Kwong, Man Kam; Li, Yi Symmetry results for reaction-diffusion equations. Differential Integral Equations 6 (1993), no. 5, 1045--1056. 35J65 (35R35) Request a Copy

Li, Yi On the positive solutions of the Matukuma equation. Duke Math. J. 70 (1993), no. 3, 575--589. 35B05 (34B15 35J60 35Q55) Request a Copy

Li, Yi Asymptotic behavior of positive solutions of equation ∆ u+K(x)u p=0 in Rn. J. Differential Equations 95 (1992), no. 2, 304--330. 35B40 (35B05 35J60) Request a Copy

Li, Yi; Ni, Wei-Ming On the asymptotic behavior and radial symmetry of positive solutions of semilinear elliptic equations in Rn. II. Radial symmetry. Arch. Rational Mech. Anal. 118 (1992), no. 3, 223--243. 35J65 (35B40 53A07) Request a Copy

Li, Yi; Ni, Wei-Ming On the asymptotic behavior and radial symmetry of positive solutions of semilinear elliptic equations in Rn. I. Asymptotic behavior. Arch. Rational Mech. Anal. 118 (1992), no. 3, 195--222. 35J65 (35B40 53A07) Request a Copy

Kwong, Man Kam; Li, Yi Uniqueness of radial solutions of semilinear elliptic equations. Trans. Amer. Math. Soc. 333 (1992), no. 1, 339--363. 35J65 (34B15 35J25) Request a Copy

Li, Yi Symmetry properties of finite total mass solutions of Matukuma equation. Nonlinear diffusion equations and their equilibrium states, 3 (Gregynog, 1989), 375--389, Progr. Nonlinear Differential Equations Appl., 7, Birkhäuser Boston, Boston, MA, 1992. 35B05 (35J60) Request a Copy

Lin, Fang-Hua; Li, Yi Boundary C1, α regularity for variational inequalities. Comm. Pure Appl. Math. 44 (1991), no. 6, 715--732. 35J85 (49J40) Request a Copy

Kaper, Hans G.; Kwong, Man Kam; Li, Yi On the positive solutions of the free-boundary problem for Emden-Fowler type equations. Partial differential equations with minimal smoothness and applications (Chicago, IL, 1990), 163--172, IMA Vol. Math. Appl., 42, Springer, New York, 1992. 35R35 (35B05 35J65) Request a Copy

Li, Yi; Ni, Wei-Ming On the existence and symmetry properties of finite total mass solutions of the Matukuma equation, the Eddington equation and their generalizations. Arch. Rational Mech. Anal. 108 (1989), no. 2, 175--194. 35J60 (85A99) Request a Copy

Li, Yi; Ni, Wei-Ming On conformal scalar curvature equations in Rn. Duke Math. J. 57 (1988), no. 3, 895--924. 58G30 (35J60) Request a Copy

Li, Yi Remarks on a semilinear elliptic equation on Rn. J. Differential Equations 74 (1988), no. 1, 34--49. 35J60 Request a Copy

Other Activities

Service
 
 
Managing Editor: Journal of Partial Differential Equations - 2008 to present
 
Conferences Organized
 
 
2006 International Conference on Partial Differential Equations and Numerical Analysis, Changsha, Hunan, 22-26 June
 
2005 HuaZhong International Conference on Nonlinear Partial Differential Equations, Zhang-Jia-Jie, P.R. China, 09-12 July
 
2005 Mini-Conference of Numerical Analysis and its Applications on the Occasion of Prof. Aixiang Huang's 70th Birthday, Changsha, Hunan, 21-23 July