Browse > Article
http://dx.doi.org/10.12941/jksiam.2013.17.017

GLOBAL EXISTENCE FOR VOLTERRA-FREDHOLM TYPE FUNCTIONAL IMPULSIVE INTEGRODIFFERENTIAL EQUATIONS  

Vijayakumar, V. (DEPARTMENT OF MATHEMATICS, INFO INSTITUTE OF ENGINEERING)
Prakash, K. Alagiri (DEPARTMENT OF MATHEMATICS, INFO INSTITUTE OF ENGINEERING)
Murugesu, R. (DEPARTMENT OF MATHEMATICS, SRMV COLLEGE OF ARTS AND SCIENCE)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.17, no.1, 2013 , pp. 17-28 More about this Journal
Abstract
In this paper, we study the global existence of solutions for the initial value problems for Volterra-Fredholm type functional impulsive integrodifferential equations. Using the Leray-Schauder Alternative, we derive conditions under which a solution exists globally.
Keywords
Leray-Schauder Alternative; a priori bounds; impulsive functional integrodifferential equations; global existence;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 S. Ntouyas, Y. Sficas and P. Tsamatos, An existence principle for the boundary value problems for the second order functional differential equations, Nonlinear Anal. TMA, 20 (1993), 215-222.   DOI   ScienceOn
2 S. Ntouyas and P. Tsamatos, Initial and boundary value problems for functional integrodifferential equations, J. Appl. Math. Stoch. Anal., 7 (1994), 191-201.   DOI   ScienceOn
3 S. Ntouyas and P. Tsamatos, Global existence for functional integrodifferential equations of delay and neutral type, Applicable Anal., 54 (1994), 251-262.   DOI
4 S. Ntouyas and I. Purnaras, Existence results for mixed Volterra-Fredholm type neutral functional integrodifferential equations in Banach spaces, Nonlinear Stud., 16 (20, (2009), 135-148.
5 B. Pachpatte, Applications of the Leray-Schauder Alternative to some Volterra integral and integrodifferential equations, Indian J. pure appl. Math., 26 (1995), 1161-1168.
6 Y.V. Rogovchenko, Impulsive evolution systems: Main results and new trends, Dynam. Contin. Discrete Impuls. Syst., 3(1) (1997), 57-88.
7 Y.V. Rogovchenko, Nonlinear impulsive evolution systems and application to population models, J. Math. Anal. Appl., 207(2) (1997), 300-315.   DOI   ScienceOn
8 A. M. Samoilenko and N.A. Perestyuk; Impulsive Differential Equations, World Scientific, Singapore, 1995.
9 S. Sivasankaran, M. Mallika Arjunan and V. Vijayakumar, Existence of global solutions for second order impulsive abstract partial differential equations, Nonlinear Anal. TMA, 74(17) (2011), 6747-6757.   DOI   ScienceOn
10 S. Sivasankaran, M. Mallika Arjunan and V. Vijayakumar, Existence of global solutions for impulsive functional differential equations with nonlocal conditions, J. Nonlinear Sci. Appl., 4(2) (2011), 102-114.
11 S. Sivasankaran, V. Vijayakumar and M. Mallika Arjunan, Existence of global solutions for impulsive abstract partial neutral functional differential equations, Int. J. Nonlinear Sci., 11(4) (2011), 412-426.
12 H.L. Tidke and M.B. Dhakne, Global existence of mild solutions of second order nonlinear Volterra integrodifferential quations in Banach spaces, Diff. Equ. Dynam. Syst., 17(4) (2009), 331-342.   DOI
13 H.L. Tidke, Existence of global solutions to nonlinear mixed Volterra-Fredholm integrodifferential equations with nonlocal conditions, Elect. J. Diff. Equ., 55 (2009), 17.
14 H.L. Tidke and M.B. Dhakne, Existence of solutions for nonlinear mixed type integrodifferential equation of second order, Surveys. Math. Appl., 5 (2010), 61-72.
15 V. Vijayakumar, S. Sivasankaran and M. Mallika Arjunan, Existence of global solutions for second order impulsive abstract functional integrodifferential equations, Dyn. Contin. Discrete Impuls. Syst., 18 (2011), 747-766.
16 V. Vijayakumar, S. Sivasankaran and M. Mallika Arjunan, Existence of solutions for double perturbed impulsive neutral functional evolution equations, J. KSIAM, 15(4) (2011), 253-265.
17 V. Vijayakumar, S. Sivasankaran and M. Mallika Arjunan, Existence of solutions for second order impulsive partial neutral functional integrodifferential equations with infinite delay, Nonlinear Stud., 19(2) (2012), 327-343.
18 V. Vijayakumar, S. Sivasankaran and M. Mallika Arjunan, Global existence for Volterra- Fredholm type neutral impulsive functional integrodifferential equations, Surveys. Math. Appl., 7 (2012), 49-68.
19 A. Anguraj and M. Mallika Arjunan, Existence of solutions for second order impulsive functional integrodifferential inclusions, For East J. Dynamical Systems, 9 (2), (2007), 265-278.
20 M. Benchohra, J. Henderson and S.K. Ntouyas, Impulsive Differential Equations and Inclusions, Hindawi Publishing Corporation, New York, 2006.
21 M. Benchohra and S.K. Ntouyas, Initial and boundary value problems for nonconvex valued multivalued functional differential equations, J. Appl. Math. Stoc. Anal., 16 (2), (2003), 191-200.   DOI   ScienceOn
22 Y. K. Chang and W. T. Li, Existence results for second order impulsive functional differential inclusions, J. Math. Anal. Appl., 301, (2005), 477-490.   DOI   ScienceOn
23 Y.K. Chang, V. Kavitha and M. Mallika Arjunan, Existence results for a second order impulsive functional differential equation with state-dependent delay, Diff. Equ. Appl., 1(3) (2009), 325-339.
24 Y.K. Chang, A. Anguraj and M. Mallika Arjunan, Existence results for impulsive neutral functional differential equations with infinite delay, Nonlinear Anal. Hybrid Systems, 2(1) (2008), 209-218.
25 M. Frigon and D. O. Regan, Boundary value problems for the second order impulsive differential equations using set-valued maps, Applicable Anal., 58 (1995), 325-333.   DOI
26 Y.K. Chang, V. Kavitha and M. Mallika Arjunan, Existence results for impulsive neutral differential and integrodifferential equations with nonlocal conditions via fractional operators, Nonlinear Anal. Hybrid Systems, 4(1) (2010), 32-43.
27 J.P.C. dos Santos, V. Vijayakumar and R. Murugesu, Existence of mild solutions for nonlocal cauchy problem for fractional neutral integro-differential equation with unbounded delay, Commun. Math. Anal., 14(1) (2013), 59-71.
28 J. Dugundji and A. Granas, Fixed point theory, Vol. 1, Matematyczne, PNW Warsawa, 1982.
29 E. Hern'andez, A second order impulsive Cauchy problem, Int. J. Math. Math. Sci., 31(8) (2002), 451-461.   DOI   ScienceOn
30 E. Hern'andez, H. R. Henriquez and M. A. McKibben, Existence results for abstract impulsive second-order neutral functional differential equations, Nonlinear Anal., 70 (2009), 2736-2751.   DOI   ScienceOn
31 E. Hern'andez, Existence results for partial neutral integrodifferential equations with nonlocal conditions, Dynam. Systems Appl., 11(2) (2002), 241-252.
32 H. R. Henriquez and C. H. V'asquez, Existence results for abstract impulsive second-order neutral functional differential equations, Nonlinear Anal., 70 (2009), 2736-2751.   DOI   ScienceOn
33 V. Laksmikantham, D. Bainov and P. S. Simenov, Theory of impulsive differential equations, Series in Modern Applied Mathematics, 6. World Scientific Publishing Co., Inc., Teaneck, NJ, 1989.
34 S. Ntouyas, Y. Sficas and P. Tsamatos, Existence results for initial value problems for neutral functional differential equations, J. Diff. Equ., 14 (1994), 527-537.