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International Symposium on Neural Networks

ISNN 2009: Advances in Neural Networks – ISNN 2009 pp 512–521Cite as

Neutral Differential Systems with Impulse and Delay

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5551))

Abstract

In this paper, we discuss a class of impulsive partial neutral functional differential inclusions with infinite delay. The existence of mild solutions of these neutral differential systems with impulse and delay is obtained by using the new nonlinear alternatives of Leray-Schauder type.

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References

  1. Benchohra, M., Gatsori, E.P., Ntouyas, S.K.: Exitence Results for Functional and Neutral Functional Integrodifferential Inclusions with Lower Semicontinuous Right-hand Side. J. Math. Anal. Appl. 281, 525–538 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Benchohra, M., Ntouyas, S.K.: Nonlocal Cauchy problems for Neutral Functional Differential and Integrodifferential Inclusions in Banach Spaces. J. Math. Anal. Appl. 258, 573–590 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. Benchohra, M., Henderson, J., Ntouyas, S.K.: Existence results for impulsive multivalued semilinear neural functional differential inclusions in Banach spaces. J. Math. Anal. Appl. 263, 763–780 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Benchohra, M., Ntouyas, S.K.: An Existence Result on Noncompact Intervals to First Order Integrodifferential Inclusions in Banach Spaces. Libertas Math. 20, 71–78 (2000)

    MathSciNet  MATH  Google Scholar 

  5. Benchohra, M., Gatsori, E.P., Ntouyas, S.K.: Controllbility of Semilinear Evolution Inclusions with Nonlocal Conditions. J. Optim. Theory Appl. 118, 493–513 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. Benchohra, M., Ntouyas, S.K.: Controllbility Results for Multivalued Semilinear Neutral Functional Differential Equations. Math. Sci. Res. J. 6, 65–77 (2002)

    MathSciNet  MATH  Google Scholar 

  7. Fitzpatrick, P.M., Petryshyn, W.V.: Fixed Point Theorems for Multivalued Noncompact Acyclic Mappings. Pacific J. Math. 54, 17–23 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  8. Deimling, K.: Multivalued Differential Equations. de Gruyter, Berlin/New York (1992)

    Google Scholar 

  9. Regan, D.: Nonlinear Alternatives for Multivalued Maps with Applications to Operator Inclusions in Abstract Spaces. Proc. of the Amer. Math. Society 127, 3557–3564 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  10. Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. In: Applied Methematical Sciences. Springer, New York (1983)

    Google Scholar 

  11. Hino, Y., Murakami, S., Naito, T.: Functional Differential Equations with Infinite Delay. Lecture Notes in Mathematics. Springer, New York (1991)

    Book  MATH  Google Scholar 

  12. Carmichael, N., Quinn, M.D.: An Approach to Nonlinear Control Problems Using Fixed-point Methods, Degree Theory, and Pseodo-Inverses. Numer. Funct. Anal. Optim. 7, 197–219 (1984-1985)

    Article  MATH  Google Scholar 

  13. Lasota, A., Opial, Z.: An Application of the Kakutani-Ky Fan Theorem in the Theory of Ordinary Differential Equations. Bull. Acad. Pol. Sci. Ser. Sci. Math. Astronom. Phys. 13, 781–786 (1965)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    Junhao Hu

  2. College of Computer Science, South Central University for Nationalities, Wuhan, 430074, China

    Junhao Hu

  3. College of Science, Huazhong Agriculture University, Wuhan, 430070, China

    Huafeng Chen

Authors
  1. Junhao Hu
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  2. Huafeng Chen
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Editor information

Editors and Affiliations

  1. Departamento de Control Automático, CINVESTAV-IPN, A.P. 14-740, Av.IPN 2508, 07360, México D.F., México

    Wen Yu

  2. Deptartment of Electrical and Computer Engineering, Stevens Institute of Technology, NJ 07030, Hoboken, USA

    Haibo He

  3. Dept. of Electrical and Computer Engineering, South Dakota School of Mines & Technology, 501 E. St. Joseph Street, Rapid City, SD 57701, USA

    Nian Zhang

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© 2009 Springer-Verlag Berlin Heidelberg

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Hu, J., Chen, H. (2009). Neutral Differential Systems with Impulse and Delay. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01507-6_59

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  • DOI: https://doi.org/10.1007/978-3-642-01507-6_59

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01506-9

  • Online ISBN: 978-3-642-01507-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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