Yihong Du

Books

  1. Y. Du, Order structure and topological methods in nonlinear partial differential equations. Vol. 1. Maximum principles and applications. Series in Partial Differential Equations and Applications, 2. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2006. (x+190 pages. ISBN: 981-256-624-4)
  2. Y. Du, Hitoshi Ishii and Wei-Yueh Lin (eds.) Recent Progress in Nonlinear Partial Differential Equations and Viscosity Solutions, World Scientific Publishing, 2009. (372 pages. ISBN: 981-283-473-7)

Papers

  1. Y. Du and Zongming Guo, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary II, submitted. (PDF file)
  2. F. Cirstea and Y. Du, Isolated singularities for weighted quasilinear elliptic equations, J. Functional Anal., to appear.
  3. Y. Du and Li Ma, A Liouville theorem for conformal Gaussian curvature type equations in $\R^2$, submitted.
  4. Y. Du and Zhigui Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42(2010), 377-405. (PDF file)
  5. Y. Du and S.B. Hsu, On a nonlocal reaction-diffusion problem arising from the modeling of phytoplankton growth, SIAM J. Math. Anal., to appear.
  6. Y. Du and R. Peng, The periodic logistic equation with spatial and temporal degeneracies, submitted.
  7. E.N. Dancer, Y. Du and Zongming Guo, Finite Morse index solutions of an elliptic equation with supercritical exponent, submitted.
  8. Y. Du, Change of environment in model ecosystems: effect of a protection zone in diffusive population models, in "Recent Progress in Nonlinear Partial Differential Equations and Viscosity Solutions", Eds. Y. Du, H. Ishii and W.Y. Lin, World Scientific Publishing, 2009. ISBN 978-981-283-473-7
  9. Y. Du and Hiroshi Matano, Convergence and sharp thresholds for propagation in nonlinear diffusion problems, J. European Math. Soc., 12(2010), 279-312. (PDF file)
  10. Y. Du, Rui Peng and Mingxin Wang, Effect of a protection zone in the diffusive Leslie predator-prey model, J. Diff. Eqns., 246(2009), 3932-3956.
  11. Y. Du, Zhaoli Liu, Angela Pistoia and Shusen Yan, Sign changing solutions with clustered layers near the origin for singularly perturbed semilinear elliptic problems on a ball, Methods and Applications of Analysis (special issure dedicated to N.S. Trudinger), 15(2008), 137-148.
  12. Y. Du and Z.M. Guo, Positive solutions of an elliptic equation with negative exponent: stability and critical power, J. Diff. Eqns., 246(2009), 2387-2414.
  13. Y. Du and S.-B. Hsu, Concentration phenomena in a nonlocal quasiliear problem modelling phytoplankton I: Existence, SIAM J. Math. Anal. 40(2008), 1419-1440.
  14. Y. Du and S.-B. Hsu, Concentration phenomena in a nonlocal quasiliear problem modelling phytoplankton II: Limiting profile, SIAM J. Math. Anal. 40(2008), 1441-1470.
  15. Y. Du, P.Y.H. Pang and M. Wang, Qualitative analysis of a predator-prey model with stage structure for the predator, SIAM J. Appl. Math., 69(2008), 596-620.
  16. Y. Du and Yoshio Yamada, On the long-time limit of positive solutions to the degenerate logistic equation, Discrete and Continuous Dynamical Systems A, 25(2009), 123-132.
  17. F. Cirstea and Y. Du, Asymptotic behavior of solutions of semilinear elliptic equations near an isolated singularity, J. Functional Anal., 250(2007),317-346.
  18. Y. Du, The heterogeneous Allen-Cahn equation in a ball: solutions with layers and spikes, J. Diff. Eqns., 244(2008), 117-169.
  19. Y. Du and Kimie Nakashima, Morse index of layered solutions to the heterogeneous Allen-Cahn equation, J. Diff. Eqns., 238(2007), 87-117.
  20. Y. Du and Xing Liang, A diffusive competition model with a protection zone, J. Diff. Eqns., 244(2008), 61-86.
  21. Y. Du and Junping Shi, Some recent results on diffusive predator-prey models in spatially heterogeneous environment, in Nonlinear Dynamics and Evolution Equations, Eds. Hermann Brunner, Xiao-Qiang Zhao and Xingfu Zou, Fields Institute Communications Vol. 48, American Math. Soc., 2006, pp 95-135.
  22. Y. Du and Junping Shi, A diffusive predator-prey model with a protection zone, J. Diff. Eqns., 229(2006), 63-91.
  23. F. Cirstea and Y. Du, Large solutions of elliptic equations with a weakly superlinear nonlinearity, J. d'Analyse Math., 103(2007), 261-277.
  24. Y. Du, Z.M. Guo and F. Zhou, Boundary blow-up solutions with interior layers and spikes in a bistable problem, Discrete and Continuous Dynamical Systems, 19(2007), 271-298.
  25. Y. Du and Lishan Liu, Remarks on the uniqueness problem of the logistic equation on the entire space, Bull. Australian Math. Soc., 73(2006), 129-137.
  26. Y. Du and Junping Shi, Allee effect and bistability in a spatially heterogeneous predator-prey model, Trans. Amer. Math. Soc., 359(2007), 4557-4593.
  27. Y. Du and M.X. Wang, Asymptotic behavior of positive steady-states to a predator-prey model, Proc. Roy. Soc. Edinburgh, 136A(2006), 759-778.
  28. Y. Du and Z-M. Guo, The degenerate logistic model and a singularly mixed boundary blow-up problem, Discrete and Continuous Dynamical Systems, 14(2006), 1-29.
  29. E.N. Dancer and Y. Du, A uniqueness theorem for a free boundary problem, Proc. Amer. Math. Soc., 134(2006), 3223-3230.
  30. Y. Du and Z.M. Guo, Boundary layer and spike layer solutions for a bistable elliptic problem with generalized boundary conditions, J. Diff. Eqns., 221(2006), 102-133.
  31. F. Cirstea and Y. Du, General uniqueness results and variation speed for blow-up solutions of elliptic equations, Proc. London Math. Soc., 91(2005), 459-482.
  32. Y. Du, Bifurcation and related topics in elliptic problems, Handbook for Partial Diff. Eqns.-Stationary Partial Differential Equations, Vol. 2, Eds. M. Chipot and P. Quittner, Elsevier, 2005, pp.127-209.
  33. Y. Du and S.J. Li, Nonlinear Liouville theorems and a priori estimates for indefinite superlinear elliptic equations, Adv. Diff. Eqns., 10(2005), 841-860.
  34. Y. Du and X.B. Pan, Multiple states and hysteresis for type I superconductors, J. Math. Physics, 46(2005), 073301(34pp).
  35. Y. Du, Multiplicity of positive solutions for an indefinite superlinear elliptic problem in R^N, Ann. Inst. Henri Poincare Anal. Non Lineaire, 21(2004), 657-672.
  36. Y. Du and S.B. Hsu, A diffusive predator-prey model in heterogeneous environment, J. Diff. Eqns., 203(2004), 331-364.
  37. Y. Du and Z.M. Guo, Symmetry for elliptic equations in a half space without strong maximum principle, Proc. Roy. Soc. Edinburgh, 134A(2004), 259-269.
  38. Y. Du, Spatial patterns for population models in a heterogeneous environment, (survey article), Taiwanese J. Math., 8(2004), 155-182.
  39. Y. Du and Z.M. Guo, Uniqueness and layer analysis for boundary blow-up solutions, J. Math. Pures Appl., 83(2004), 739-763.
  40. Y. Du and S. Yan, Boundary blow-up solutions with a spike layer, J. Diff. Eqns., 205(2004), 156-184.
  41. Y. Du, Asymptotic behavior and uniqueness results for boundary blow-up solutions, Diff. Integral Eqns., 17(2004), 819-834.


Last updated: June 2009

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