On some singular nonlinear evolution equations

  • Marco Luigi Bernardi
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1223)


We study, in this paper, a class of singular or degenerate nonlinear abstract differential equations of parabolic type. We prove, for such equations, an existence and uniqueness result, in the framework of suitable Banach weighted spaces.


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  1. [1]
    C. BAIOCCHI and M.S. BAOUENDI, Singular evolution equations, J. of Funct.Anal., 25 (1977), 103–120.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    M.L. BERNARDI, Su alcune equazioni d'evoluzione singolari, Boll.Un. Mat.Ital., 5, 13-B (1976), 498–517.MathSciNetzbMATHGoogle Scholar
  3. [3]
    F.E. BROWDER, Nonlinear initial value problems, Annals of Math., 82, (1965), 51–87.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    R.W. CARROLL and R.E. SHOWALTER, "Singular and Degenerate Cauchy Problems", Science and Engineering, n.127, Academic Press, New York, 1976.Google Scholar
  5. [5]
    G. DA PRATO and P. GRISVARD, Sommes d'opérateurs linéaires et équations différentielles opérationnelles, J.Math.Pures et Appl., 54 (1975), 305–387.zbMATHGoogle Scholar
  6. [6]
    G. DA PRATO and P. GRISVARD, On an abstract singular Cauchy problem, Comm. in P.D.E., 3 (11) (1978), 1077–1082.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    A.FAVINI, Degenerate and singular evolution equations in Banach space, to appear on Math.Ann.Google Scholar
  8. [8]
    K.L. KUTTLER JR., A degenerate nonlinear Cauchy problem, Appl.Anal., 13 (1982), 307–322.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    K.L. KUTTLER JR., Implicit evolution equations, Appl.Anal., 16(1983), 91–99.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    J.E. LEWIS and C. PARENTI, Abstract singular parabolic equations, Comm. in P.D.E., 7 (3) (1982), 279–324.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    J.L. LIONS, "Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires", Dunod-Gauthier Villars, Paris, 1969.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Marco Luigi Bernardi
    • 1
  1. 1.Dipartimento di MatematicaUniversità di PaviaPaviaItaly

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