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On the solvability of nonlinear equations involving abstract and differential operators

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Functional Analysis Methods in Numerical Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 701))

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References

  1. H. Brezis, Équations et in équations non-lineares dans les espaces en dualité, Ann. Inst. Fourier, Grenoble, 18 (1968), 115–175.

    Article  MathSciNet  MATH  Google Scholar 

  2. F.E. Browder, Existence theory for boundary value problems for quasilinear elliptic systems with strongly nonlinear lower order terms, Proc. Symp. in Pure Math. 23 (1973), 269–286.

    Article  MathSciNet  MATH  Google Scholar 

  3. _____, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proc. Symp. in Pure Math, AMS, Vol. 18, Part 2 (1976).

    Google Scholar 

  4. F.E. Browder and W.V. Petryshyn, Approximation methods and the generalized topological degree for nonlinear maps in Banach spaces, J. Functional Anal., 3 (1969), 217–245.

    Article  MathSciNet  MATH  Google Scholar 

  5. K.J. Brown, Some operator equations with an infinite number of solutions, Quart. J. Math (Oxford) (2), 25 (1974), 195–212.

    Article  MathSciNet  MATH  Google Scholar 

  6. B. Calvert and J.R.L. Webb, An existence theorem for quasimonotone operators, Accad. Naz. Dei Lincei, Ser. 8, 50 (1971), 362–368.

    MathSciNet  MATH  Google Scholar 

  7. E.N. Dancer, Boundary-value problems for ordinary differential equations on infinite intervals, Proc. London Math. Soc. 30 (1975), 76–94.

    Article  MathSciNet  MATH  Google Scholar 

  8. N. Dunford and J.T. Schwartz, Linear Operators, Part II; Interscience, New York, 1963.

    MATH  Google Scholar 

  9. P.M. Fitzpatrick, Surjectivity results for nonlinear mappings from a Banach space to its dual, Math. Ann. 204 (1973), 177–188.

    Article  MathSciNet  MATH  Google Scholar 

  10. P.M. Fitzpatrick and W.V. Petryshyn, Positive eigenvalues for nonlinear multivalued noncompact operators with applications to differential operators, J. Differential Equations, 22 (1976), 428–441.

    Article  MathSciNet  MATH  Google Scholar 

  11. D.G. De Figueiredo, The Dirichlet problem for nonlinear elliptic equations: A Hilbert space approach

    Google Scholar 

  12. A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York, 1969.

    MATH  Google Scholar 

  13. P. Hess, On nonlinear mappings of monotone type homotopic to odd operators, J. Functional Anal., 11 (1972), 138–167.

    Article  MathSciNet  MATH  Google Scholar 

  14. P.M. Hess, Théorème d'existence pour des perturbations d'opérateurs maximaux monotones, C.R. Acad. Sc. Paris, t.275 (1972), Ser. A, 1171–1173.

    MathSciNet  MATH  Google Scholar 

  15. J. Leray and J.-L. Lions, Quelques résultats de Višik sur les problemes elliptiques non linéaires par les méthodes de Minty-Browder, Bull. Soc. Math. Frances 93 (1965), 97–107.

    MathSciNet  MATH  Google Scholar 

  16. P.S. Milojevic and W.V. Petryshyn, Continuation and surjectivity theorems for uniform limits of A-proper mappings with applications, J. Math. Anal. Appl. (to appear).

    Google Scholar 

  17. _____, Continuation theorems and the approximation-solvability of equations involving multivalued A-proper mappings, J. Math. Anal. Appl. (to appear).

    Google Scholar 

  18. G. Minty, Monotone (nonlinear) operators in Hilbert space, Duke Math. J. 29 (1962), 341–346.

    Article  MathSciNet  MATH  Google Scholar 

  19. R.D. Nussbaum, The fixed point index for local condensing maps, Ann. Math. Pura Appl. (4) 89 (1971), 217–258.

    Article  MathSciNet  MATH  Google Scholar 

  20. W.V. Petryshyn, On nonlinear equations involving pseudo-A-proper mappings and their uniform limits with applications, J. Math. Anal. Appl. 38 (1972), 672–720.

    Article  MathSciNet  MATH  Google Scholar 

  21. _____, On the approximation-solvability of equations involving A-proper and pseudo-A-proper mappings, Bull. Amer. Math. Soc., 81 (1975), 223–312.

    Article  MathSciNet  MATH  Google Scholar 

  22. _____, On the relationship of A-properness to mappings of monotone type with applications to elliptic equations, Fixed Point Theory and its Application (ed. S. Swaminathan), Academic Press, N.Y.), 1976, 149–174.

    Google Scholar 

  23. _____, Fixed point theorems for various classes of 1-set-contractive and 1-ball-contractive mappings in Banach spaces, Trans. Amer. Math. Soc. 182 (1973), 323–352.

    MathSciNet  MATH  Google Scholar 

  24. _____, Fredholm alternative for nonlinear A-proper mappings with applications to nonlinear elliptic boundary value problems, J. Functional Anal. 18 (1975), 288–317.

    Article  MathSciNet  MATH  Google Scholar 

  25. W.V. Petryshyn and P.M. Fitzpatrick, On 1-set and 1-ball contractions with applications to perturbation problems for nonlinear bijective maps and linear Fredholm maps, Bull. UMI, (4) 7 (1973), 102–124.

    MathSciNet  MATH  Google Scholar 

  26. B.N. Sadovskii, Ultimately compact and condensing mappings, Uspehi Mat. Nauk 27 (1972), 81–146.

    MathSciNet  Google Scholar 

  27. C.A. Stuart, Some bifurcation theory for k-set-contractions, Proc. London Math. Soc. 27 (1973), 531–550.

    Article  MathSciNet  MATH  Google Scholar 

  28. J.F. Toland, Global bifurcation theory via Galerkin method, University of Essex, Fluid Mechanics Reas. Inst. Report. No. 69 (1976).

    Google Scholar 

  29. M.M. Vainberg, Variational Methods for the Study of Nonlinear Operators, Holden-Day, San Francisco, 1964.

    MATH  Google Scholar 

  30. J.R.L. Webb, Mapping and fixed point theorems for nonlinear operators in Banach spaces, Proc. London Math. Soc. (3) 20 (1970), 451–468.

    Article  MathSciNet  MATH  Google Scholar 

  31. J.R.L. Webb, On a characterization of k-set-contractions, Accad. Naz. Dei Lincei, Ser. 8, 50 (1971), 358–361.

    Google Scholar 

  32. F. Wille, Monotone Operatoren mit Störungen, Arch. Rat. Mech. Anal. 46 (1971), 369–388.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Rutgers University, New Brunswick, N. J., USA

    W. V. Petryshyn

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  1. W. V. Petryshyn
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M. Zuhair Nashed

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© 1979 Springer-Verlag

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Petryshyn, W.V. (1979). On the solvability of nonlinear equations involving abstract and differential operators. In: Nashed, M.Z. (eds) Functional Analysis Methods in Numerical Analysis. Lecture Notes in Mathematics, vol 701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062083

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  • DOI: https://doi.org/10.1007/BFb0062083

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09110-3

  • Online ISBN: 978-3-540-35530-4

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