Partial Functional Evolution Equations with Infinite Delay

  • Saïd Abbas
  • Mouffak Benchohra
Part of the Developments in Mathematics book series (DEVM, volume 39)


In this chapter, we provide sufficient conditions for the existence of the unique mild solution on the positive half-line \(\mathbb{R}_{+}\) for some classes of first order partial functional and neutral functional differential evolution equations with infinite delay.


Infinite Delay Functional Development Mild Solution Partial Evolution Equations Abstract Evolution Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 15.
    R.P. Agarwal, S. Baghli, M. Benchohra, Controllability of mild solutions on semiinfinite interval for classes of semilinear functional and neutral functional evolution equations with infinite delay. Appl. Math. Optim. 60, 253–274 (2009)CrossRefGoogle Scholar
  2. 16.
    N.U. Ahmed, Semigroup Theory with Applications to Systems and Control. Pitman Research Notes in Mathematics Series, vol. 246 (Longman Scientific & Technical, Harlow; Wiley, New York, 1991)Google Scholar
  3. 32.
    C. Avramescu, Some remarks on a fixed point theorem of Krasnoselskii. Electron. J. Qual. Differ. Equ. 5, 1–15 (2003)Google Scholar
  4. 33.
    S. Baghli, M. Benchohra, Uniqueness results for evolution equations with infinite delay in Fréchet spaces. Fixed Point Theory 9, 395–406 (2008)Google Scholar
  5. 36.
    S. Baghli, M. Benchohra, K. Ezzinbi, Controllability results for semilinear functional and neutral functional evolution equations with infinite delay. Surv. Math. Appl. 4, 15–39 (2009)Google Scholar
  6. 93.
    N. Carmichael, M.D. Quinn, An approach to nonlinear control problems using the fixed point methods, degree theory and pseudo-inverses. Numer. Funct. Anal. Optim. 7, 197–219 (1984–1985)Google Scholar
  7. 108.
    K. Ezzinbi, Existence and stability for some partial functional differential equations with infinite delay. Electron. J. Differ. Equ. 2003(116), 1–13 (2003)Google Scholar
  8. 112.
    A. Freidman, Partial Differential Equations (Holt, Rinehat and Winston, New York, 1969)Google Scholar
  9. 116.
    M. Frigon, A. Granas, Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet. Ann. Sci. Math. Québec 22(2), 161–168 (1998)Google Scholar
  10. 128.
    A. Granas, J. Dugundji, Fixed Point Theory (Springer, New York, 2003)CrossRefGoogle Scholar
  11. 141.
    Y. Hino, S. Murakami, Total stability in abstract functional differential equations with infinite delay. Electronic Journal of Qualitative Theory of Differential Equations. Lecture Notes in Mathematics, vol. 1473 (Springer, Berlin, 1991)Google Scholar
  12. 145.
    F. Kappel, W. Schappacher, Some considerations to the fundamental theory of infinite delay equations. J. Differ. Equ. 37, 141–183 (1980)CrossRefGoogle Scholar
  13. 149.
    S.G. Krein, Linear Differential Equations in Banach Spaces (The American Mathematical Society, Providence, 1971)Google Scholar
  14. 168.
    A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations (Springer, New York, 1983)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Saïd Abbas
    • 1
  • Mouffak Benchohra
    • 2
  1. 1.Laboratoire de MathématiquesUniversité de SaïdaSaïdaAlgeria
  2. 2.Department of MathematicsUniversity of Sidi Bel AbbesSidi Bel AbbesAlgeria

Personalised recommendations