Existence results for impulsive neutral functional integrodifferential equation with infinite delay
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Authors
T. Gunasekar
- School of Advanced Sciences, Fluid Dynamics Division, VIT University, Vellore-632 014, Tamil Nadu, India.
F. Paul Samuel
- Department of Mathematics and Physics, University of Eastern Africa, Baraton, Eldoret 2500--30100, Kenya.
M. Mallika Arjunan
- Department of Mathematics, C. B. M College of Arts and Science, Kovaipudur, Coimbatore-641 042, Tamil Nadu, India.
Abstract
In this paper, we study the existence of mild solutions for a impulsive semilinear neutral functional integrodifferential equations with infinite delay in Banach spaces. The results are obtained by using the Hausdorff
measure of noncompactness. Examples are provided to illustrate the theory.
Impulsive differential equation, Neutral functional differential equation, Mild solution,
Hausdorff measures of noncompactness.
Share and Cite
ISRP Style
T. Gunasekar, F. Paul Samuel, M. Mallika Arjunan, Existence results for impulsive neutral functional integrodifferential equation with infinite delay, Journal of Nonlinear Sciences and Applications, 6 (2013), no. 4, 234--243
AMA Style
Gunasekar T., Samuel F. Paul, Arjunan M. Mallika, Existence results for impulsive neutral functional integrodifferential equation with infinite delay. J. Nonlinear Sci. Appl. (2013); 6(4):234--243
Chicago/Turabian Style
Gunasekar, T., Samuel, F. Paul, Arjunan, M. Mallika. "Existence results for impulsive neutral functional integrodifferential equation with infinite delay." Journal of Nonlinear Sciences and Applications, 6, no. 4 (2013): 234--243
Keywords
- Impulsive differential equation
- Neutral functional differential equation
- Mild solution
- Hausdorff measures of noncompactness.
MSC
References
-
[1]
R. Agarwal, M. Meehan, D. O'Regan , Fixed point theory and applications, in: Cambridge Tracts in Mathematics, Cambridge University Press, New York, (2001), 178-179.
-
[2]
R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina, B. N. Sadovskii, Measure of noncompactness and condensing operators, Translated from the Russian by A. Iacob, Basel; Boston, Berlin : Birkhauser (1992)
-
[3]
J. M. Ayerbe, T. D. Benavides, G. L. Acedo, Measure of noncmpactness in in metric fixed point theorem, Birkhauser, Basel (1997)
-
[4]
S. Baghlt, M. Benchohra , Perturbed functional and neutral functional evolution equations with infinite delay in Frechet spaces, Electron. J. Differ. Equ. , 69 (2008), 1-19.
-
[5]
J. Banas, K. Goebel, Measure of Noncompactness in Banach Space, in: Lecture Notes in Pure and Applied Matyenath, Dekker, New York (1980)
-
[6]
J. Banas, W. G. El-Sayed, Measures of noncompactness and solvability of an integral equation in the class of functions of locally bounded variation, J. Math. Anal. and Appl., 167 (1992), 133-151.
-
[7]
J. Banas, A. Martinon, Measure of noncmpactness in Banach sequnence spaces, Portugalie Math. , 52 (1995), 131-138.
-
[8]
G. Emmanuele, Measures of weak noncompactness and fixed point theorems, Bull. Math. Soc. Sci. Math. R. S. Roumanie, 25 (1981), 353-358.
-
[9]
Z. Fan, Q. Dong, G. Li , Semilinear differential equations with nonlocal conditions in Banach spaces, Int. J. Nonlinear Sci., 2 (2006), 131-139.
-
[10]
M. Benchohra, J. Henderson, S. K. Ntouyas , Existence results for impulsive multivalued semilinear neutral functional inclusions in Banach spaces , J. Math. Anal. Appl., 263 (2001), 763-780.
-
[11]
M. Benchohra, S. Djebali, T. Moussaoui , Boundary value problems for double perturbed first order ordinary differential systems , Electron. J. Qual.Theory Differ. Equ. , 11 (2006), 1-10.
-
[12]
F. S. De Blasi, On a property of the unit sphere in a Banach space, Bull. Math. Soc. Sci. Math. R.S. Roumanie, 21 (1977), 259-262.
-
[13]
Y. K. Chang, A. Anguraj, M. Mallika Arjunan, Existence results for impulsive neutral functional differential equations with infinite delay , Nonlinear Anal. Hybrid Syst., 2 (2008), 209-218.
-
[14]
Q. Dong, Z. Fan, G. Li , Existence of solutions to nonlocal neutral functional differential and integrodifferential equations, Int. J. Nonlinear Sci., 5 (2008), 140-151.
-
[15]
Q. Dong, Double perburbed evolution equations with infinite delay in Banach spaces, J. Yangzhou Univ. (Natural Science Edition), 11 (2008), 7-11.
-
[16]
J. K. Hale, J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac., 21 (1978), 11-41.
-
[17]
E. Hernandez, A second-order impulsive Cauchy problem, Int. J. Math. Math. Sci., 31 (2002), 451-461.
-
[18]
E. Hernandez, H. R. Henriquez, Impulsive partial neutral differential equations, Appl. Math. Lett., 19 (2006), 215-222.
-
[19]
E. Hernandez, M. Rabello, H. Henriaquez, Existence of solutions for impulsive partial neutral functional differential equations, J. Math. Anal. Appl., 331 (2007), 1135-1158.
-
[20]
E. Hernandez, Existence results for a class of semi-linear evolution equations, Electron. J. Differ. Equ., 201 (2001), 1-14.
-
[21]
E. Hernandez, H. R. Henriquez , Existence results for partial neutral functional differential equations with unbounded delay, J. Math. Anal. Appl. , 221 (1998), 452-475.
-
[22]
E. Hernandez, H. R. Henriquez , Existence of periodic solutions of partial neutral functional differential equations with unbounded delay , J. Math. Anal.Appl., 221 (1998), 499-522.
-
[23]
Y. Hino, S. Murakami, T. Naito, Functional-Differential Equations with Infinite Delay , in: Lecture Notes in Math., vol. 1473, Springer-Verlag, Berlin (1991)
-
[24]
V. Kavitha, M. Mallika Arjunan, C. Ravichandran , Existence results for impulsive sysyems with nonlocal conditions in banach spaces, J. Nonlinear Sci.Appl., 2 (2011), 138-151.
-
[25]
J. H. Liu, Nonlinear impulsive evolution equations, Dyn. Contin. Discrete Impuls. Syst., 6 (1999), 77-85.
-
[26]
V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, in: Series in Modern Appl. Math., 6 World Scientific Publ., Teaneck, NJ (1989)
-
[27]
M. Mallika Arjunan, V. Kavitha, S. Selvi , Existence results for impulsive differential equations with nonlocal conditions via measures of noncompactness, J. Nonlinear Sci.Appl., 5 (2012), 195-205.
-
[28]
F. Paul Samuel, K. Balachandran, Existence Results for Impulsive Quasilinear Integrodifferential Equations in Banach Spaces, Vietnam J. Math., 38 (2010), 305-321.
-
[29]
R. Ye , Existence of solutions for impulsive partial neutral functional differential equation with infinite delay, Nonlinear Anal., 73 (2010), 155-162.
-
[30]
C. C. Travis, G. F. Webb, Existence and stability for partial functional differential equations, Trans. Amer. Math. Soc., 200 (1974), 395-418.
-
[31]
G. F. Webb , Autonomos nonlinear functional differential equations and nonlinear semigroups, J. Math. Anal. Appl. , 46 (1974), 1-12.
-
[32]
Y. V. Rogovchenko, Impulsive evolution systems: main results and new trends, Dyn. Contin. Discrete Impuls. Syst., 3 (1997), 57-88.
-
[33]
Y. V. Rogovchenko, Nonlinear impulse evolution systems and applications to population models, J. Math. Anal. Appl., 207 (1997), 300-315.