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Range of nonlinear perturbations of linear operators with an infinite dimensional kernel

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Ordinary and Partial Differential Equations

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References

  1. H. BREZIS, "Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert", Mathematics Studies 5, North-Holland, Amsterdam, 1973.

    MATH  Google Scholar 

  2. H. BREZIS and F.E. BROWDER, Nonlinear integral equations and systems of Hammerstein type, Advances in Math. 18 (1975) 115–147.

    Article  MathSciNet  MATH  Google Scholar 

  3. H. BREZIS et A. HARAUX, Image d'une somme d'opérateurs monotones et applications, Israel J. Math. 23 (1976) 165–186.

    Article  MathSciNet  MATH  Google Scholar 

  4. H. BREZIS and L. NIRENBERG, Characterizations of the ranges of some nonlinear operators and applications to boundary value problems, Ann. Scuola Norm. Sup. Pisa, to appear.

    Google Scholar 

  5. F.E. BROWDER, Existence of periodic solutions for nonlinear equations of evolution, Proc. Nat. Acad. Sci. U.S.A. 53 (1965) 1100–1103.

    Article  MathSciNet  MATH  Google Scholar 

  6. F.E. BROWDER, Periodic solutions of nonlinear equations of evolution in infinite dimensional spaces, in "Lectures in Differential Equations", vol. 1, A.K. Aziz ed., Van Nostrand, New York, 1969, 71–96.

    Google Scholar 

  7. F.E. BROWDER, "Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces", Proc. Symp. Pure Math., vol. XVII, part 2, Amer. Math. Soc., Providence, R.I., 1976.

    Book  MATH  Google Scholar 

  8. L. CESARI, Functional analysis, nonlinear differential equations and the alternative method, in "Nonlinear Functional Analysis and Differential Equations", L. Cesari, R. Kannan and J. Schuur ed., M. Dekker, New York, 1976, 1–197.

    Google Scholar 

  9. L. CESARI and R. KANNAN, An abstract existence theorem at resonance, Proc. Amer. Math. Soc. 63 (1977) 221–225.

    Article  MathSciNet  MATH  Google Scholar 

  10. D.G. DE FIGUEIREDO and C.P. GUPTA, Non-linear integral equations of Hammerstein type with indefinite linear kernel in a Hilbert space, Indag. Math. 34 (1972) 335–344.

    Article  MathSciNet  MATH  Google Scholar 

  11. S. FUCIK, "Ranges of Nonlinear Operators", 5 volumes, Universitas Carolina Pragensis, Prague, 1977.

    MATH  Google Scholar 

  12. S. FUCIK, J. NECAS, J. SOUCEK, Vl. SOUCEK, "Spectral Analysis for Nonlinear Operators", Lecture Notes in Math. no 346, Springer, Berlin, 1973.

    Book  MATH  Google Scholar 

  13. R.E. GAINES and J. MAWHIN, "Coincidence Degree and Nonlinear Differential Equations", Lecture Notes in Math. no 568, Springer, Berlin, 1977.

    MATH  Google Scholar 

  14. J. LERAY et J. SCHAUDER, Topologie et équations fonctionnelles, Ann. Sci. Ec. Norm. Sup. 51 (1934) 45–78.

    MathSciNet  MATH  Google Scholar 

  15. J. MAWHIN, Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mappings in locally convex topological vector spaces, J. Differential Equations 12 (1972) 610–636.

    Article  MathSciNet  MATH  Google Scholar 

  16. J. MAWHIN, Contractive mappings and periodically perturbed conservative systems, Arch. Math. (Brno) 12 (1976) 67–73.

    MathSciNet  MATH  Google Scholar 

  17. J. MAWHIN, Solutions périodiques d'équations aux dérivées partielles hyperboliques non linéaires, in "Mélanges Th. Vogel", B. Rybak, P. Janssens et M. Jessel ed., Presses Univ. de Bruxelles, Bruxelles, 1978, 301–315.

    Google Scholar 

  18. J. MAWHIN, Landesman-Lazer's type problems for nonlinear equations, Confer. Sem. Mat. Univ. Bari no 147, 1977.

    Google Scholar 

  19. J. MAWHIN and M. WILLEM, Periodic solutions of nonlinear differential equations in Hilbert spaces, in "Proceed. Equadiff 78", Firenze 1978, to appear.

    Google Scholar 

  20. K. SCHMITT and R. THOMPSON, Boundary value problems for infinite systems of second-order differential equations, J. Differential Equations 18 (1975) 277–295.

    Article  MathSciNet  MATH  Google Scholar 

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W. N. Everitt

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© 1980 Springer-Verlag

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Mawhin, J., Willem, M. (1980). Range of nonlinear perturbations of linear operators with an infinite dimensional kernel. In: Everitt, W.N. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091380

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  • DOI: https://doi.org/10.1007/BFb0091380

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  • Print ISBN: 978-3-540-10252-6

  • Online ISBN: 978-3-540-38346-8

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