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A simplified approach to the existence and stability problem of a functional evolution equation in a general Banach space

Part of the Lecture Notes in Mathematics book series (LNM,volume 1076)

Keywords

  • Weak Solution
  • Functional Differential Equation
  • Nonlinear Evolution Equation
  • Unique Weak Solution
  • General Banach Space

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References

  1. Crandall, M., T. Liggett: Generation of semigroups of nonlinear transformations on general Banach spaces, Amer. J. Math. 93 (1971), 265–298.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Crandall, M., A. Pazy: Nonlinear evolution equations in Banach spaces, Israel J. Math. 11 (1972), 57–94.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. Dyson, J., R. Villella-Bressan: Functional differential equations and nonlinear evolution operators, Proc. Royal Soc. Edinburgh, 75A (1975/76), 223–234.

    MathSciNet  MATH  Google Scholar 

  4. Dyson, J., R. Villella-Bressan: Semigroups of translations associated with functional and functional differential equations, Proc. Royal Soc. Edinburgh, 82A (1979), 171–188.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Evans, L.: Nonlinear evolution equations in an arbitrary Banach space, Israel J. Math. 26 (1977), 1–42.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Kartsatos, A.G., M.E. Parrott: Convergence of the Kato approximants for evolution equations involving functional perturbations, J. Diff. Equations 47 (1983), 358–377.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Kartsatos, A.G., M.E. Parrott: Existence of solutions and Galerkin approximations for nonlinear functional evolution equations, Tohoku Math. J. 34 (1982), 509–523.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Kartsatos, A.G., M.E. Parrott: A method of lines for a nonlinear abstract functional differential equation, Trans. A.M.S., to appear.

    Google Scholar 

  9. Webb, G.F.: Asymptotic stability for abstract nonlinear functional differential equations, Proc. Am. Math. Soc. 54 (1976), 225–230.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1984 Springer-Verlag

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Kartsatos, A.G., Parrott, M.E. (1984). A simplified approach to the existence and stability problem of a functional evolution equation in a general Banach space. In: Kappel, F., Schappacher, W. (eds) Infinite-Dimensional Systems. Lecture Notes in Mathematics, vol 1076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072771

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  • DOI: https://doi.org/10.1007/BFb0072771

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13376-6

  • Online ISBN: 978-3-540-38932-3

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