Several Results on Nonsmooth Analysis

  • Xianling Fan
Part of the Mathematics and Its Applications book series (MAIA, volume 356)


In this paper we summarize the author’s several results on nonsmooth analysis.


Periodic Solution Open Subset Hamiltonian System Lipschitz Function Topological Degree 
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  1. [1]
    Ambrosetti A., Coti-Zelati V., Closed orbits of fixed energy for singular Hamiltonian systems, Arch. Rat. Mech. Anal., 112 (1990),339–362.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    Aubin J. P., Cellina A., Differentiate Inclusions, Springer-Verlag.Berlin, 1984.Google Scholar
  3. [3]
    Benci V., Giannoni F., Periodic solution of prescribed energy for a class of Hamiltonian systems with singular potentials, J. Diff. Eq., 82 (1989), 60–70.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Berestycki H., Lasry J., Mancini G., Ruf B., Existence of multiple periodic orbits in star-shaped Hamiltonian surfaces, Comm. Pure Appl. Math., 38 (1985), 253–289.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    Borisovich Yu., Zviagin V., Sapronov Yu., Nonlinear Fredholm maps arid Leray-Schauder theory. Uspekhi Mat. Nauk, 32: 4 (1977), 3–54.zbMATHGoogle Scholar
  6. [6]
    Chang K. C., Critical Point Theory and Its Applications, Shanghai Science and Technology Press, Shanghai, 1986. (Chinese).zbMATHGoogle Scholar
  7. [7]
    Chang K. C., Variational methods for nondifferentiable functionals and their application to PDE., J. Math. Anal. Appl., 80 (1981), 102–129.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    Chen W. Y., Nonlinear Functional Analysis, Gansu Renmin Press, Lanzhou, 1982. (Chinese).Google Scholar
  9. [9]
    Chen W. Y., Fan X. L., Implicit Function Theorems, Lanzhou Univ. Press, Lanzhou, 1986. (Chinese).Google Scholar
  10. [10]
    Clarke F. H., Optimization and Nonsmooth Analysis, John Wiley, Sons, Inc., 1983.zbMATHGoogle Scholar
  11. [11]
    Fan X. L., The C 1-admissible approximation for Lipschitz functions and the Hamiltonian inclusions, (Research Announcements) Advances in Math. (China), 20: 1 (1991), 127–128.zbMATHGoogle Scholar
  12. [12]
    Fan X. L., A Viterbo-Hofer-Zehnder type result for Hamiltonian inclusions, Ann. Faculte Sci. Toulouse Math., 12: 3 (1991), 365–372.zbMATHCrossRefGoogle Scholar
  13. [13]
    Fan X. L., The set-valued Fredholm mappings and topological degree, Chinese Quarterly J. Math., 6: 4 (1991), 68–71. (Chinese).Google Scholar
  14. [14]
    Fan X.L., The necessary and sufficient conditions for Lipschitz local homeomorphism, Chin. Ann. of Math., 13 B: l (1992), 40–45.Google Scholar
  15. [15]
    Fan X. L., Existence of multiple periodic orbits on star-shaped Lipschitz-Hamiltonian surfaces, J. Diff. Eq., 98: 1 (1992), 91–110.zbMATHCrossRefGoogle Scholar
  16. [16]
    Fan X. L., The essential critical points of lipschitz functionals, J. Math. Research Exposition, 14: 4 (1994), 557–560. (Chinese).zbMATHGoogle Scholar
  17. [17]
    Fan X. L., Liu B. S., The essential critical points of minimax type of Lipschitz functionals, J. Lanzhou Univ. (Natur. Sci.), 31: 1 (1995), 1–4. (Chinese).MathSciNetzbMATHGoogle Scholar
  18. [18]
    Fan X. L., Qin C. L., The C 0-Fredholm maps and topological degree, J. Lanzhou Univ. (Natur. Sci.), 30: 4 (1994), 1–4. (Chinese).zbMATHGoogle Scholar
  19. [19]
    Fan X. L., Liu B. S., The C 1-admissible approximation for Lipschitz functions and the Hamiltonain inclusions, J. Lanzhou Univ. (Natur. Sci.), 29: 3 (1993), 38–42. (Chinese).MathSciNetzbMATHGoogle Scholar
  20. [20]
    Fan X. L., Wang B. X., Remarks on periodic solutions of prescibed energy for singular Hamiltonian systems, Houston J. Math., 17: 3 (1991), 385–393.MathSciNetzbMATHGoogle Scholar
  21. [21]
    Hofer H., Zehnder E., Periodic solutions on hypersurfaces and a result by C. Viterbo, Invent. Math., 90 (1987), 1–9.MathSciNetzbMATHCrossRefGoogle Scholar
  22. [22]
    Rabinowitz P. H., Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math., 31 (1978), 157–184.MathSciNetCrossRefGoogle Scholar
  23. [23]
    Shi S. Z., Nonsmooth analysis, Adv. in Math. (China), 15: 1 (1986), 9–21. (Chinese).zbMATHGoogle Scholar
  24. [24]
    Viterbo C., A proof of the Weinstein conjecture in R 2n, Ann. Inst. H. Poincare, Anal, non Lineaire, 4 (1987), 337–356.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Xianling Fan
    • 1
  1. 1.Department of MathematicsLanzhou UniversityLanzhouChina

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