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On existence of solutions of impulsive nonlinear functional neutral integro-differential equations with nonlocal condition

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the present paper, we investigate the existence, uniqueness and continuous dependence of mild solutions of an impulsive neutral integro-differential equations with nonlocal condition in Banach spaces. We use Banach contraction principle and the theory of fractional power of operators to obtain our results.
Wydawca
Rocznik
Strony
413--423
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
  • School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University, Nanded-431606, India, rupalisjain@gmail.com
autor
  • Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431004, India, mbdhakne@yahoo.com
Bibliografia
  • [1] H. Akca, A. Boucherif, V. Covachev, Impulsive functional differential equations with nonlocal conditions, Int. J. Math. Math. Sci. 29(5) (2002), 251–256.
  • [2] A. Anguraj, K. Karthikeyan, Existence of solutions for impulsive functional differential equations with nonlocal conditions, Nonlinear Anal. 70 (2009), 2717–2721.
  • [3] M. Benchora, J. Henderson, Existence results for impulsive multivalued semilinear neutral functional differential inclusions in Banach spaces, J. Math. Anal. Appl. 263 (2001), 763–780.
  • [4] K. Balachandran, J. Y. Park, Nonlocal Cauchy problem for Sobolev type functional integro-differential equations, Bull. Korean Math. Soc. 39(1) (2002), 561–569.
  • [5] K. Balachandran, J. Y. Park, Existence of a mild solution of a functinal integro-differential equations with nonlocal condition, Bull. Korean Math. Soc. 38(1) (2001), 175–182.
  • [6] L. Byszewski, On mild solution of a semilinear functional differential evolution nonlocal problem, J. Appl. Math. Stochastic Anal. 10(3) (1997), 265–271.
  • [7] L. Byszewski, H. Akca, Existence of solutions of a semilinear functional evolution nonlocal problem, Nonlinear Anal. 34 (1998), 65–72.
  • [8] L. Byszewski, V. Lakshamikantham, Theorems about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Anal. 40 (1990), 11–19.
  • [9] J. P. Daur, K. Bhalchandran, Existance of solutions of nonlinear neutral integro-differential equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), 93–105.
  • [10] M. B. Dhakne, K. D. Kucche,Existence of mild solution of mixed Volterra-Fredholm functional integrodifferential equation with nonlocal condition, Appl. Math. Sci. 5(8) (2011), 359–366.
  • [11] E. Hernandez, M. Hernan, R. Henriquez, Impulsive partial neutral differential equations , Appl. Math. Lett. 19 (2006), 215–222.
  • [12] R. S. Jain, M. B. Dhakne, On global existence of solutions for abstract nonlinear functional integro-differential equations with nonlocal condition, Contemp. Math. Stat. 1 (2013), 44–53.
  • [13] R. S. Jain, M. B. Dhakne, On mild solutions of nonlocal semilinear functional integro-differential equations, Malaya J. Math. 3(1) (2013), 27–33.
  • [14] J. Liang, Z. Fan, Nonlocal impulsive Cauchy problems for evolution equations , Advances in Difference Equations, Vol. 2011, Article ID 784161, 17 pages.
  • [15] V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
  • [16] B. Liu, Controllability of impulsive neutral functional differential inclusions with infinte delay, Nonlinear Anal. 60 (2005), 1533–1552.
  • [17] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York, 1983.
  • [18] A. M. Samoilenko, N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.
  • [19] S. C. Ji, S. Wen, Nonlocal Cauchy problem for impulsive differential equations in Banach spaces, Int. J. Nonlinear Sci. 10(1) (2010), 88–95.
  • [20] S. Sivasankaran, V. Vijaykumar, M. M. Arjunan, Existence of global solutions for impulsive abstract partial neutral functional differential equations, Int. J. Nonlinear Sci. 11(4) (2011), 412–426.
  • [21] V. Vijaykumar, S. Sivasankaran, M. M. Arjunan, Global existence for Volterra-Fredholm type neutral impulsive functional integro-differential equations, Surveys Math. Appl. 7 (2012), 49–68.
Typ dokumentu
Bibliografia
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