Nonlocal cauchy problem for delay integrodifferential equations of Sobolev type in Banach spaces

Applied Mathematics Letters

Volumn 15, Issue 7, 2002, Pages 845-854

  Balachandran, K ^a   Park, J Y ^b   Chandrasekaran, M ^a  

^a BHARATHIAR UNIVERSITY   (India)

^b Pusan National University   (South Korea)

Author keywords

Delay integrodifferential equations; Existence theorem; Fixed point theorem; Nonlocal condition

Indexed keywords

EID: 31244434224     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(02)00052-6     Document Type: Article

References (27)

1. D. Bahuguna, Quasilinear integrodifferential equations in Banach spaces, Nonlinear Analysis, Theory, Methods and Applications 24, 175-183 (1995).
2. M.B. Dhakne and B.C. Pachpatte, On a general class of abstract functional integrodifferential equations, Indian Journal of Pure and Applied Mathematics 19, 728-746 (1988).
3. G. Gripenberg, Global existence of solutions of Volterra integrodifferential equations of parabolic type, Journal of Differential Equations 102, 382-390 (1993).
4. M.L. Heard, A class of hyperbolic Volterra integrodifferential equations, Nonlinear Analysis, Theory, Methods and Applications 8, 79-93 (1984).
5. M.L. Heard and S.M. Rankin III, A semilinear parabolic Volterra integrodifferential equation, Journal of Differential Equations 71, 201-233, (1988).
6. M.L. Heard and S.M. Rankin III, Nonlinear Volterra integrodifferential equations, Journal of Mathematical Analysis and Applications 188, 569-589, (1994).
7. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, (1983).
8. L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, Journal of Mathematical Analysis and Applications 162, 494-505 (1991).
9. L. Byszewski, Existence, uniqueness and asymptotic stability of weak and strong solutions of functional-differential abstract nonlocal Cauchy problems, Dynamic Systems and Applications 5, 595-606 (1996).
10. L. Byszewski, On weak solutions of functional-differential abstract nonlocal Cauchy problems, Annales Polonici Mathematici 2, 163-170, (1997).
11. L. Byszewski, On a mild solution of a semilinear functional-differential evolution nonlocal problems, Journal of Applied Mathematics and Stochastic Analysis 10, 265-271 (1997).
12. L. Byszewski and H. Akca, Existence of solutions of a semilinear functional differential evolution nonlocal problem, Nonlinear Analysis, Theory, Methods and Applications 34, 65-712 (1998).
13. K. Balachandran, Existence and uniqueness of mild and strong solutions of nonlinear integrodifferential equation with nonlocal condition, Differential Equations and Dynamical-Systems 6, 159-165 (1998).
14. K. Balachandran and S. Ilamaran, Existence and uniqueness of mild and strong solutions of a Volterra integrodifferential equation with nonlocal conditions, Tamkang Journal of Mathematics 28, 93-100 (1997).
15. J.P. Dauer and K. Balachandran, Existence of solutions for an integrodifferential equation with nonlocal condition in Banach spaces, Libertas Mathematica 16, 133-143 (1996).
16. S. Ilamaran and K. Balachandran, Existence and uniqueness of mild and strong solutions of an integrodifferential equation with nonlocal condition, Libertas Mathematica 15, 119-127 (1995).
17. Y. Lin and J.H. Liu, Semilinear integrodifferential equations with nonlocal Cauchy problem, Nonlinear Analysis, Theory, Method and Applications 26, 1023-1033 (1996).
18. S.K. Ntouyas and P.Ch. Tsamatos, Global existence for semilinear evolution equations with nonlocal conditions, Journal of Mathematical Analysis and Applications 210, 679-987 (1997).
19. S.K. Ntouyas and P.Ch. Tsamatos, Global existence for semilinear evolution integrodifferential equations with delay and nonlocal conditions, Applicable Analysis 64, 99-105 (1997).
20. K. Deng, Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions, Journal of Mathematical Analysis and Applications 179, 630-637 (1993).
21. H. Brill, A semilinear Sobolev evolution equation in a Banach space, Journal of Differential Equations 24, 412-425 (1977).
22. J.E. Lagnese, Exponential stability of solutions of differential equation of Sobolev type, SIAM Journal of Mathematical Analysis 3, 625-636 (1972).
23. J.H. Lightboure III and S.M. Rankin III, A partial functional differential equation of Sobolev Type, Journal of Mathematical Analysis and Applications 93, 328-337 (1983).
24. R.E. Showalter, Existence and representation theorems for a semilinear Sobolev equation in Banach space, SIAM Journal of Mathematical Analysis 3, 527-543 (1972).
25. R.E. Showalter, A nonlinear parabolic-Sobolev equation, Journal of Mathematical Analysis and Applications 50, 183-190 (1975).
26. K. Balachandran, D.G. Park and Y.C. Kwun, Nonlinear integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces, Communications of the Korean Mathematical Society 14, 223-231 (1999).
27. H. Schaefer, Uber die methode der a priori schranken, Mathematische Annalem 129, 415-416 (1955).