Yihong Du

Publications up to 2003:

1. A note on a theorem of H. Amann, Chinese Science Bull., 31(1986), 636.
2. On the fixed point index of positive operators, J. Math.(Wuhan), 6(1986), 91-98. [Math. Review 87h:47118]
3. Multiple solutions of increasing condensing operator equations, Northeast Math. J., 3(1987), 199-309. [Math. Review 89i:47116]
4. Positive solutions of nonlinear eigenvalue problems and its applications, J. Shandong Univ., 22(1987), 25-33.
5. Multiple solutions of nonlinear eigenvalue problems and its applications, J. Shandong Univ., 22(1987), 34-40.
6. Total order minihedral cones, J. Sys. Sci. and Math., 8(1988), 19-24. [Math. Review 89i:46022]
7. Multiple solutions of eigenvalue problems with increasing operators, Acta Math. Sinica, 31(1988), 21-28. [Math. Review 89g: 58033]
8. Nonzero solutions and eigenvectors of nonlinear equations, Acta Math. Sinica, 32(1989), 76-85. [Math. Review 90i:47065]
9. Fixed points of a class of non-compact operators and applications, Acta Math. Sinica, 32(1989), 618-627. [Math. Review 91c:47116]
10. Multiple fixed points of increasing maps, J. Math.(Wuhan), 9(1989), 81-86. [Math. Review 90g:47089]
11. A deformation lemma and its applications, Chinese Science Bull., 35(1990), 96-97. [Math. Review 92m:58018]
12. On the global structure of the positive solution set of a nonlinear operator, Acta Math. Sinica, 33(1990), 445-455. [Math. Review 92d: 47078]
13. Fixed points of increasing operators in ordered Banach spaces and applications, Appl. Anal., 38(1990), 1-20. [Math. Review 92f:47057]
14. A deformation lemma and some critical point theorems, Bull. Aust. Math. Soc., 43(1991), 161-168. [Math. Review 92b:58034]
15. The structure of the solution set of a class of nonlinear eigenvalue problems, J. Math. Anal. Appl., 170(1992), 567-580. [Math. Review 93m:47068]
16. Nontrivial solutions of super-linear Sturm-Liouville problems, Acta Math. Sinica, 35(1992), 721-728. [Math. Review 94c:34027]
17. Critical point theorems with relaxed boundary condition and applications, Bull. Austr. math. Soc., 47(1993), 108-118. [Math. Review 94a:58033]
18. (With K.J. Brown) Bifurcation and monotonicity in competition reaction-diffusion systems, Nonlinear Anal., TMA. 23(1994), 1-13. [Math. Review 95h:35112]
19. (With E.N. Dancer) Competing species equations with diffusion, large interactions and jumping nonlinearities, J. Diff. Eqns., 114(1994), 434-475. [Math. Review 95i:35296]
20. (With E.N. Dancer) Existence of changing sign solutions for some semilinear problems with jumping nonlinearities at zero, Proc. Roy. Soc. Edinburgh, 124A(1994), 1165-1176. [Math. Review 96b:35062]
21. (With E.N. Dancer) Positive solutions for a three species competition system with diffusion, Part I, General existence results, Nonlinear Anal., TMA., 24(1995), 337-357. [Math. Review 96c:92028]
22. (With E.N. Dancer) Positive solutions for a three species competition system with diffusion, Part II, The case of equal birth rates, Nonlinear Anal., TMA., 24(1995), 359-373. [Math. Review 96c:92029]
23. Uniqueness results for the gap equation in the theory of supperconductivity, Diff. and Integral Eqns., 8(1995), 309-324. [Math. Review 95i:82104]
24. (With E.N. Dancer) Multiple solutions of some semilinear elliptic equations via the generalized Conley index, J. Math. Anal. Appl., 189(1995), 848-871. [Math. Review 96a:35059 ]
25. (With E.N. Dancer) On sign-changing solutions of certain semilinear elliptic problems, Appl. Anal., 56(1995), 193-206.
26. Uniqueness, multiplicity and stability for positive solutions of a pair of reaction-diffusion equations, Proc. Roy. Soc. Edinburgh, 126A(1996), 777-809.
27. Positive periodic solutions of a competitor-competitor-mutualist model, Diff. Int. Eqns., 9(1996), 1043-1066.
28. Bifurcation from semitrivial solution bundles and applications to certain equation systems, Nonlinear Analysis, 27(1996), 1407-1435.
29. (With E.N. Dancer) The generalized Conley index and multiple solutions of semilinear elliptic problems, Abstract and Applied Analysis, 1(1996), 103-135.
30. (With Y. Lou) Some uniqueness and exact multiplicity results for a predator-prey model, Trans. Amer. Math. Soc., 349(1997), 2443-2475.
31. (With E.N. Dancer) A note on multiple solutions of some semilinear elliptic problems, J. Math. Anal. Appl., 211(1997), 626-640.
32. (With Y. Lou) S-shaped global bifurcation curve and Hopf bifurcation of positive solutions to a predator-prey model, J. Diff. Eqns., 144(1998), 390-440.
33. On Dancer's fixed point index formulas, Diff. Integral Eqns., 13(2000), 145-158.
34. A degree theoretic approach to N-species periodic competition systems on the whole $R^n$, Proc. Roy. Soc. Edinburgh, 129A(1999), 295-318.
35. (With Y. Lou) Proof of a conjecture for the perturbed Gelfand equation from combustion theory, J. Diff. Eqns. 173(2001), 213-230.
36. (With Q. Huang) Blow-up solutions for a class of semilinear elliptic and parabolic equations, SIAM J. Math. Anal., 31(1999), 1-18.
37. (With Z-M. Guo) The degenerate logistic model and a singularly mixed boundary blow-up problem, Discrete and Continuous Dynamical Systems, 14(2006),1-29.
38. Exact multiplicity and S-shaped bifurcation curve for some semilinear elliptic problems from combustion theory, SIAM J. Math. Anal., 32(2000), 707-733.
39. (With Yuan Lou) Qualitative behaviour of positive solutions of a predator-prey model: effects of saturation, Proc. Royal Soc. Edinburgh, 131A(2001), 321-349.
40. Effects of a degeneracy in the competition model, part I: classical and generalized steady-state solutions, J. Diff. Eqns., 181(2002), 92-132.
41. Effects of a degeneracy in the competition model, part II: perturbation and dynamical behaviour, J. Diff. Eqns., 181(2002), 133-164.
42. (With Shujie Li) Positive solutions with prescribed patterns in some simple semilinear equations, Diff. Integral Eqns. 15(2002), 805-822.
43. (With Li Ma) Logistic type equations on R^N by a squeezing method involving boundary blow-up solutions, J. London Math Soc., 64(2001), 107-124.
44. Bifurcation from infinity in a class of nonlocal elliptic problems, Diff. Integral Eqns., 15(2002), 587-606.
45. (With Li Ma) Positive solutions of an elliptic partial differential equation on R^N, J. Math. Anal. Appl., 271(2002), 409-425.
46. (with E.N. Dancer) Effects of certain degeneracies in the predator-prey model, SIAM J Math. Anal., 34(2002), 292-314.
47. (with E.N. Dancer) On a free boundary problem arising from population biology, Indiana Univ. Math. J., 52 (2003), 51-68.
48. (with E.N. Dancer and L. Ma) Asymptotic behaviour of positive solutions of some elliptic problems, Pacific J. Math., 210(2003), 215-228.
49. (with L. Ma) Some remarks related to De Giorgi's conjecture, Proc. Amer Math Soc., 131(2003), 2415-2422.
50. (with Z.M. Guo) Boundary blow-up solutions and their applications in quasilinear elliptic problems, J. d'Analyse Math., 89(2003), 277-302.
51. (with Z.M. Guo) Liouville type results and eventual flatness of positive solutions for p-Laplacian equations, Adv. Diff. Eqns., 7(2002), 1479-1512.
52. (with E.N. Dancer) Some remarks on Liouville type results for quasilinear elliptic equations, Proc. Amer. Math. Soc.,131 (2003), 1891-1899.
53. (with T. Ouyang) Bifurcation from infinity induced by a degeneracy in semilinear equations, Advanced Nonlinear Studies, 2(2002), 117-132.
54. (with Y. Guo) Mountain pass solutions and an indefinite superlinear elliptic problem on R^N, Topological Methods in Nonl. Anal., 22(2003), 69-92.
55. Realization of prescribed patterns in the competition model, J. Diff. Eqns., 193(2003), 147-179.
56. (with W. Dong) Unbounded principal eigenfunctions and the logistic equation on R^N, Bull. Australian Math. Soc., 67(2003), 413-427.
57. Boundary blow-up solutions and their applications, in Topological Methods, Variational Methods, and Their Applications, Eds., H. Brezis, K.C. Chang, S. Li and P. Rabinowitz, World Scientific, 2003, pp. 89-97.

Last updated: July 2005.