Existence results for an impulsive neutral integro-differential equations in Banach spaces

Usha, Venkatesh; Baleanu, Dumitru; Arjunan, Mani Mallika

doi:10.2478/auom-2019-0043

Abstract

In this manuscript we investigate the existence of mild solution for a abstract impulsive neutral integro-differential equation by using semi-group theory and Krasnoselskii-Schaefer fixed point theorem in different approach. At last, an example is also provided to illustrate the obtained results.

References

[1] A. Anguraj, M. Mallika Arjunan and E. Hernandez, Existence results for an impulsive neutral functional differential equation with state-dependent delay, Applicable Analysis, 86(7)(2007), 861–872.10.1080/00036810701354995
Search in Google Scholar Back to article
[2] A. Anguraj and K. Karthikeyan, Existence of solutions for impulsive neutral functional differential equations with nonlocal conditions, Nonlinear Analysis: Theory, Methods & Applications, 70(7)(2009), 2717–2721.10.1016/j.na.2008.03.059
Search in Google Scholar Back to article
[3] K. Balachandran and N. Annapoorani, Existence results for impulsive neutral evolution integrodifferential equations with infinite delay, Nonlinear Analysis: Hybrid Systems, 3(2009), 674–684.10.1016/j.nahs.2009.06.004
Search in Google Scholar Back to article
[4] M. Benchohra, J. Henderson and S. Ntouyas, Impulsive Differential Equations and Inclusions, Hindawi Publishing Corporations, Contemporary Mathematics and Its Applications, Volume 2, 2006.10.1155/9789775945501
Search in Google Scholar Back to article
[5] T. Cardinali and P. Rubbioni, Impulsive semilinear differential inclusion: Topological structure of the solution set and solutions on non-compact domains, Nonlinear Analysis: Theory, Methods & Applications, 69(1)(2008), 73–84.10.1016/j.na.2007.05.001
Search in Google Scholar Back to article
[6] A. Chadha and Dwijendra N Pandey, Existence results for an impulsive neutral integro-differential equation with infinite delay via fractional operators, Malaya Journal of Matematik 2(3)(2014), 203–214.10.1155/2014/780636
Search in Google Scholar Back to article
[7] Y.K. Chang, A. Anguraj and M. Mallika Arjunan, Existence results for impulsive neutral functional differential equations with infinite delay, Nonlinear Analysis: Hybrid Systems, 2(1)(2008), 209–218.10.1016/j.nahs.2007.10.001
Search in Google Scholar Back to article
[8] Y.K. Chang, A. Anguraj and M. Mallika Arjunan, Existence results for non-densely defined neutral impulsive differential inclusions with nonlocal conditions, Journal of Applied Mathematics and Computation, 28(1)(2008), 79–91.10.1007/s12190-008-0078-8
Search in Google Scholar Back to article
[9] Y.K. Chang, A. Anguraj and K. Karthikeyan, Existence for impulsive neutral integro-differential inclusions with nonlocal initial conditions via fractional operators, Nonlinear Analysis: Theory, Methods & Applications, 71(10)(2009), 4377–438610.1016/j.na.2009.02.121
Search in Google Scholar Back to article
[10] K. Ezzinbi, Xianlong Fu and Khalid Hilal, Existence and regularity in the - norm for some neutral partial differential equations with nonlocal conditions, Nonlinear Analysis: Theory, Methods & Applications, 67(5)(2007), 1613–1622.10.1016/j.na.2006.08.003
Search in Google Scholar Back to article
[11] Z. Fan and G. Li, Existence results for semilinear differential equations with nonlocal and impulsive conditions, Journal of Functional Analysis, 258(5)(2010), 1709–1727.10.1016/j.jfa.2009.10.023
Search in Google Scholar Back to article
[12] J.K. Hale, Partial neutral functional-differential equations, Romanian Journal of Pure and Applied Mathematics, 39(4)(1994), 339–344.
Search in Google Scholar Back to article
[13] J.K. Hale and S.M. Verduyn Lunel, Introduction to Functional-Differential Equations, Applied Mathematical Sciences, Springer-Verlag, New York, 99(1993).10.1007/978-1-4612-4342-7
Search in Google Scholar Back to article
[14] E. Hernandez and Donald O’Regan, Existence results for a class of abstract impulsive differential equations, Bulletin of Australian Mathematical Society, 87(3)(2013), 366–385.10.1017/S0004972713000154
Search in Google Scholar Back to article
[15] E. Hernandez, Jair Silverio dos Santos and Katia A.G. Azevedo, Existence of solutions for a class of abstract differential equations with nonlocal conditions, Nonlinear Analysis: Theory, Methods & Applications, 74(7)(2011), 2624–2634.10.1016/j.na.2010.12.018
Search in Google Scholar Back to article
[16] E. Hernandez and Donald O’Regan, On a new class of abstract neutral differential equations, Journal of Functional Analysis, 261(12)(2011), 3457–3481.10.1016/j.jfa.2011.08.008
Search in Google Scholar Back to article
[17] E. Hernandez and H.R. Henriquez, Impulsive partial neutral differential equations, Applied Mathematics Letters, 19(3)(2006), 215–222.10.1016/j.aml.2005.04.005
Search in Google Scholar Back to article
[18] L. Hu and Y. Ren, Existence results for impulsive neutral stochastic functional Integro-differential equations with infinite delay, Acta Applicandae Mathematicae, 111(3)(2010), 303–317.10.1007/s10440-009-9546-x
Search in Google Scholar Back to article
[19] V. Lakshmikantham, D. Bainov and P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, (1989).10.1142/0906
Search in Google Scholar Back to article
[20] N.Y. Nadaf and M. Mallika Arjunan, Existence and controllability results for damped second order impulsive neutral functional differential systems with state-dependent delay in Banach spaces, Malaya Journal of Matematik, 1(1)(2013), 70–85.10.26637/mjm101/008
Search in Google Scholar Back to article
[21] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 44, 1983.10.1007/978-1-4612-5561-1
Search in Google Scholar Back to article
[22] C. Parthasarathy and M. Mallika Arjunan, Existence results for impulsive neutral stochastic functional integro-differential systems with infinite delay, Malaya Journal of Matematik 1(1)(2012), 26–41.10.26637/mjm0101/005
Search in Google Scholar Back to article
[23] S. Selvarasu, P. Kalamani and M. Mallika Arjunan, Approximate controllability of nonlocal impulsive fractional neutral stochastic integrodifferential equations with state-dependent delay in Hilbert spaces, Malaya Journal of Matematik, 4(4)(2016), 571–598.10.1186/s13662-016-0885-4
Search in Google Scholar Back to article
[24] A. Vinodkumar, Existence and uniqueness of solutions of random impulsive differential equations, Malaya Journal of Matematik, 1(1)(2012), 8–13.10.26637/mjm0101/002
Search in Google Scholar Back to article
[25] J. Wu and H. Xia, Rotating waves in neutral partial functional-differential equations, Journal of Dynamics and Differential Equations, 11(2)(1999), 209–238.10.1023/A:1021973228398
Search in Google Scholar Back to article
[26] J. Wu and H. Xia, Self-sustained oscillations in a ring array of coupled loss less transmission lines, Journal of Differential Equations, 124(1)(1996), 247–278.10.1006/jdeq.1996.0009
Search in Google Scholar Back to article
[27] J. Wu, Theory and Applications of Partial Functional-Differential Equations, Applied Mathematical Sciences, Springer- Verlag, Newyork, 119, 1996.10.1007/978-1-4612-4050-1
Search in Google Scholar Back to article

Existence results for an impulsive neutral integro-differential equations in Banach spaces

Abstract

Paradigm

My account