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On the Unique Solvability of Hammerstein Integral Equations with Non-Symmetric Kernels

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Recent Trends in Nonlinear Analysis

Summary

Some elementary results about Hammerstein integral equations with non-symmetric kernels are proved by means of Minty’s monotonicity principle.

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References

  1. H.Amann:Ein Existenz-und Eindeutigkeitssatz für die Hammersteinsche Gleichung in BanachräumenMath. Zeitschr.111 (1965), 175–190

    Article  MathSciNet  Google Scholar 

  2. J.AppellP. P.Zabrejko:Nonlinear Superposition OperatorsCambridge University Press, Cambridge 1990

    Book  MATH  Google Scholar 

  3. C. L.DolphG. J.Minty:On nonlinear integral equations of Hammerstein typein:Nonlinear Integral Equations [Ed.: P. M.Anselone], Univ. of Wisconsin, Madison 1974, 99–154

    Google Scholar 

  4. A.Hammerstein:Nichtlineare Integralgleichungen nebst AnwendungenActa Math.54 (1930), 117–176

    Article  MathSciNet  MATH  Google Scholar 

  5. P.Hess:On nonlinear equations of Hammerstein type in Banach spacesProc. Amer. Math. Soc.30, 2 (1971), 308–312

    Article  MathSciNet  Google Scholar 

  6. L. V.KantorovichG. P.Akilov:Functional Analysis [in Russian], Fizmatgiz, Moscow 1978; Engl. transl.: Pergamon Press, Oxford 1982

    Google Scholar 

  7. M. A.Krasnosel’skij:Topological Methods in the Theory of Nonlinear Integral Equations[in Russian], Gostekhizdat, Moscow 1956; Engl. transl.: Macmillan, New York 1964

    Google Scholar 

  8. M. A.Krasnosel’skijJa. B.Rutitskij:Convex Functions and Orlicz Spaces [in Russian], Fizmatgiz, Moscow 1958; Engl. transl.: Noodhoff, Groningen 1961

    Google Scholar 

  9. M. A.Krasnosel’skijJa. B.Rutitskij :Orlicz spaces and nonlinear integral equations [in Russian], Trudy Moskov. Matem. Obshch.7 (1958), 63–120

    Google Scholar 

  10. M. A.Krasnosel’skijP. P.Zabrejko:Geometrical Methods of Nonlinear Analysis [in Russian], Nauka, Moscow 1975; Engl. transl.: Springer, Berlin 1984

    Book  Google Scholar 

  11. G.Minty:Monotone nonlinear operators in Hilbert spacesDuke Math. J.29 (1962), 341–346

    Article  MathSciNet  MATH  Google Scholar 

  12. D.PascaliS.Sburlan:Nonlinear Mappings of Monotone TypeEdit. Acad., Bucharest 1978

    MATH  Google Scholar 

  13. M. M.Vajnberg:The Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations[in Russian], Nauka, Moscow 1972; Engl. transl.: Halsted Press, Jerusalem 1973

    Google Scholar 

  14. P. P.ZabrejkoA. I.Povolotskij:Remarks on existence theorems for so­lutions of Hammerstein equations [in Russian], Uchen. Zap. Leningrad. Gos. Ped. Inst.404 (1971), 374–379

    Google Scholar 

  15. P. P.ZabrejkoA. I.Povolotskij:The Hammerstein operator and Orlicz spaces [in Russian], Kachestv. Pribl. Metody Issled. Operat. Uravn. (Jaroslavl’)2 (1977), 39–51

    Google Scholar 

  16. P. P.ZabrejkoA. I.PovolotskijE. I.Smirnov:On two classes of linear operators in Hilbert spaces [in Russian], Kachestv. Pribl. Metody Issled. Operat. Uravn. (Jaroslavl’)7 (1982), 90–93

    Google Scholar 

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Al caro amico Alfonso, con l’affetto di sempre (anche di più)

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Appell, J., De Pascale, E., Zabrejko, P.P. (2000). On the Unique Solvability of Hammerstein Integral Equations with Non-Symmetric Kernels. In: Appell, J. (eds) Recent Trends in Nonlinear Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 40. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8411-2_3

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  • DOI: https://doi.org/10.1007/978-3-0348-8411-2_3

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9556-9

  • Online ISBN: 978-3-0348-8411-2

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