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Abstrakty
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
Czasopismo
Rocznik
Tom
Strony
413--423
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
- School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University, Nanded-431606, India
autor
- Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431004, India
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
Identyfikator YADDA
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