Controllability of mixed Volterra-Fredholm-type integro-differential systems in Banach space

Journal of the Franklin Institute

Volumn 344, Issue 1, 2007, Pages 12-21

  Chalishajar, D N ^a  

^a GUJARAT UNIVERSITY   (India)

Author keywords

Controllability; Leray Schauder alternative; Semi linear mixed Volterra Fredholm type integro differential system

Indexed keywords

CONTROLLABILITY; FUNCTION EVALUATION; INTEGRODIFFERENTIAL EQUATIONS; LINEAR EQUATIONS; MATHEMATICAL OPERATORS; THEOREM PROVING;

LERAY SCHAUDER ALTERNATIVE; PRIORI BOUNDS; SEMI-LINEAR MIXED VOLTERRA-FREDHOLM TYPE INTEGRO DIFFERENTIAL SYSTEM;

NONLINEAR SYSTEMS;

EID: 33846578595     PISSN: 00160032     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfranklin.2006.04.002     Document Type: Article

References (15)

1. Ntouyas S.K., and Tsamatos P.Ch. Global existence for semi-linear evolution equations with nonlocal conditions. J. Math. Anal. Appl. 210 (1997) 679-687
2. Chukwu E.N., and Lenhart S.M. Controllability questions for nonlinear systems in abstract Banach spaces. J. Optim. Theory Appl. 68 (1991) 437-462
3. Quinn M.D., and Carmichael N. An approach to nonlinear control problems using fixed point methods, degree theory and pseudo-inverse. Numer. Funct. Anal. Optim. 7 (1984/1985) 197-219
4. Balachandran K., Daur J.P., and Balasubramaniam P. Controllability of nonlinear integro-differential systems in Babach spaces. J. Optim. Theory Appl. 84 (1995) 83-91
5. Balachandran K., Daur J.P., and Balasubramaniam P. Controllability of semi-linear integro-differential systems in Babach spaces. J. Math. Syst. Estimations Control 6 (1996) 477-480
6. Balachandran K., and Sakthivel R. Controllability of integro-differential system in Banach spaces. J. Appl. Math. Comput. 118 (2001) 63-71
7. Schaefer H. Uber die Methode der a priori Schranken. Math. Ann. 129 (1955) 415-416
8. Dugunji J., and Granas A. Fixed Point Theory vol.1 (1982), Monografie Mathematyczne, PWN, Warsaw
9. Dhakne M.B., and Lamb G.B. Existence result for an abstract nonlinear integro-differential equations. Ganit: J. Bangladesh Math. Soc. 21 (2001)
10. Pachpatte B.G. Applications of the Leray-Schauder alternative to some Volterra integral and integro-differential equations. Indian J. Pure Appl. Math. 26 12 (1995) 1161-1168
11. Pachpatte B.G. On mixed Volterra-Fredholm type integral equations. Indian J. Pure. Appl. Math. 17 4 (1986) 488-496
12. Dhakne M.B., and Kendre S.D. On abstract nonlinear mixed Volterra-Fredholm integro-differential equations. Presented Paper in the International Conference at IIT-Bombay, 11-13 December (2004)
13. Burton T.A. Volterra Integral and Differential Equations (1983), Academic Press, New York
14. Dajun G., Laxmikantham V., and Xinzhi L. Nonlinear Integral Equations in Abstract Spaces (1996), Kluwer Academic Publishers, Netherlands
15. Pazy A. Semigroups of linear Operators and Applications to Partial Differential Equations (1983), Springer, New York