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Existence and controllability for nondensely defined partial neutral functional differential inclusions

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Abstract

We give sufficient conditions for the existence of integral solutions for a class of neutral functional differential inclusions. The assumptions on the generator are reduced by considering nondensely defined Hille-Yosida operators. Existence and controllability results are established by combining the theory of addmissible multivalued contractions and Frigon’s fixed point theorem. These results are applied to a neutral partial differential inclusion with diffusion.

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References

  1. N. Abada, M. Benchohra, H. Hammouche: Existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions. J. Differ. Equations 246 (2009), 3834–3863.

    Article  MATH  MathSciNet  Google Scholar 

  2. N. Abada, M. Benchohra, H. Hammouche, A. Ouahab: Controllability of impulsive semilinear functional differential inclusions with finite delay in Fréchet spaces. Discuss. Math., Differ. Incl. Control Optim. 27 (2007), 329–347.

    Article  MATH  MathSciNet  Google Scholar 

  3. M. Adimy, K. Ezzinbi: A class of linear partial neutral functional differential equations with nondense domain. J. Differ. Equations 147 (1998), 285–332.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Adimy, K. Ezzinbi: Existence and linearized stability for partial neutral functional differential equations with nondense domains. Differ. Equ. Dyn. Syst. 7 (1999), 371–417.

    MATH  MathSciNet  Google Scholar 

  5. M. Belmekki, M. Benchohra, K. Ezzinbi, S. Ntouyas: Existence results for semilinear perturbed functional differential equations of neutral type with infinite delay. Mediterr. J. Math. 7 (2010), 1–18.

    Article  MATH  MathSciNet  Google Scholar 

  6. M. Belmekki, M. Benchohra, L. Górniewicz, S. K. Ntouyas: Existence results for perturbed semilinear functional differential inclusions with infinite delay. Nonlinear Anal. Forum 13 (2008), 135–156.

    MATH  MathSciNet  Google Scholar 

  7. M. Belmekki, M. Benchohra, S. K. Ntouyas: Existence results for semilinear perturbed functional differential equations with nondensely defined operators. Fixed Point Theory Appl. 2006 (2006), 13 pages, Article ID 43696.

  8. M. Benchohra, L. Górniewicz, S. K. Ntouyas, A. Ouahab: Controllability results for nondensely defined semilinear functional differential equations. Z. Anal. Anwend. 25 (2006), 311–325.

    Article  MATH  MathSciNet  Google Scholar 

  9. M. Benchohra, A. Ouahab: Controllability results for functional semilinear differential inclusions in Fréchet spaces. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 61 (2005), 405–423.

    Article  MATH  MathSciNet  Google Scholar 

  10. C. Castaing, M. Valadier: Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics 580, Springer, Berlin, 1977.

    MATH  Google Scholar 

  11. G. Da Prato, E. Sinestrari: Differential operators with non dense domain. Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 14 (1987), 285–344.

    MATH  Google Scholar 

  12. M. Frigon: Fixed point results for multivalued contractions on gauge spaces. Set Valued Mappings with Applications in Nonlinear Analysis (R. Agarwal et al., eds.). Ser. Math. Anal. Appl. 4, Taylor & Francis, London, 2002, pp. 175–181.

    Google Scholar 

  13. J. K. Hale: Partial neutral functional differential equations. Rev. Roum. Math. Pures Appl. 39 (1994), 339–344.

    MATH  MathSciNet  Google Scholar 

  14. J. Henderson, A. Ouahab: Existence results for nondensely defined semilinear functional differential inclusions in Fréchet spaces. Electron. J. Qual. Theory Differ. Equ. 2005 (2005), 17 pages.

  15. M. E. Hernandez: A comment on the papers: Controllability results for functional semilinear differential inclusions in Fréchet spaces and Controllability of impulsive neutral functional differential inclusions with infinite delay. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 66 (2007), 2243–2245.

    Article  MATH  Google Scholar 

  16. E. N. Mahmudov: Approximation and Optimization of Discrete and Differential Inclusions. Elsevier Insights, Elsevier, Amsterdam, 2011.

    MATH  Google Scholar 

  17. E. N. Mahmudov, D. Mastaliyeva: Optimization of neutral functional-differential inclusions. J. Dyn. Control Syst. 21 (2015), 25–46.

    Article  MathSciNet  Google Scholar 

  18. B. S. Mordukhovich, L. Wang: Optimal control of neutral functional-differential inclusions. SIAM J. Control Optimization 43 (2004), 111–136.

    Article  MATH  MathSciNet  Google Scholar 

  19. J. Wu: Theory and Applications of Partial Functional Differential Equations. Applied Mathematical Sciences 119, Springer, New York, 1996.

    MATH  Google Scholar 

  20. J. Wu, H. Xia: Self-sustained oscillations in a ring array of coupled lossless transmission lines. J. Differ. Equations 124 (1996), 247–278.

    Article  MATH  MathSciNet  Google Scholar 

  21. J. Wu, H. Xia: Rotating waves in neutral partial functional differential equations. J. Dyn. Differ. Equations 11 (1999), 209–238.

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Khalil Ezzinbi.

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Ezzinbi, K., Rhali, S.L. Existence and controllability for nondensely defined partial neutral functional differential inclusions. Appl Math 60, 321–340 (2015). https://doi.org/10.1007/s10492-015-0098-2

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