The non-local cauchy problem for semilinear integrodifferential equations with deviating argument

Proceedings of the Edinburgh Mathematical Society

Volumn 44, Issue 1, 2001, Pages 63-70

  Balachandran, K ^a   Chandrasekaran, M ^a  

^a BHARATHIAR UNIVERSITY   (India)

Author keywords

Deviating argument; Existence of solutions; Integrodifferential equation; Resolvent operator

Indexed keywords

EID: 23044534151     PISSN: 00130915     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0013091598001060     Document Type: Article

References (18)

1. K. BALACHANDRAN, On a Volterra integral equation with deviating arguments, J. Appl. Math. Stock. Analysis 3 (1990), 263-266.
2. K. BALACHANDRAN AND M. CHANDRASEKARAN, Existence of solution of a delay differential equation with nonlocal condition, Indian J. Pure Appl. Math. 27 (1996), 443-449.
3. K. BALACHANDRAN AND S. ILAMARAN, Existence and uniqueness of mild and strong solutions of a semilinear evolution equation with nonlocal conditions, Indian J. Pure Appl. Math. 25 (1994), 411-418.
4. L. BYSZEWSKI, Strong maximum principles for parabolic nonlinear problems with nonlocal inequalities together with integrals, J. Appl. Math. Stock. Analysis 3 (1990), 65-79.
5. L. BYSZEWSKI, Existence and uniqueness of solutions of nonlocal problems for hyperbolic equation uxt = F(t,x,u,ux), J. Appl. Math. Stock. Analysis 3 (1990), 163-168.
6. L. BYSZEWSKI, Theorems about the existence and uniqueness of continuous solution of nonlocal problem for nonlinear hyperbolic equation, Appl. Analysis 40 (1991), 173-180.
7. L. BYSZEWSKI, Strong maximum principles for parabolic nonlinear problems with nonlocal inequalities together with arbitrary functions, J. Math. Analysis Appl. 156 (1991), 457-470.
8. L. BYSZEWSKI, Uniqueness criterion for solution to abstract nonlocal Cauchy problem, J. Appl. Math. Stoch. Analysis 162 (1991), 49-54.
9. L. BYSZEWSKI, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Analysis Appl. 162 (1992), 494-505.
10. L. BYSZEWSKI, Existence of approximate solution to abstract nonlocal Cauchy problem, J. Appl. Math. Stoch. Analysis 5 (1992), 363-374.
11. L. BYSZEWSKI AND V. LAKSHMIKANTHAM, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Analysis 40 (1990), 11-19.
12. C. CORDUNEANU, Integral equations and applications (Cambridge University Press, 1991).
13. R. GRIMMER, Resolvent operators for integral equations in a Banach space, Trans. Am. Math. Soc. 273 (1982), 333-349.
14. R. GRIMMER AND J. Liu, Liapunov-Razumikhin methods for integrodifferential equations in Hubert space, in Delay and differential equations, pp. 9-24 (World Scientific, London, 1992).
15. G. GRIPENBERG, S. O. LONDON AND O. STAFFANS, Volterra integral and functional equations (Cambridge University Press, 1990).
16. D. JACKSON, Existence and uniqueness of solutions to semilinear nonlocal parabolic equations, J. Math. Analysis Appl. 172 (1993), 256-265.
17. Y. LlN AND J. H. Liu, Semilinear integrodifferential equations with nonlocal Cauchy problem, Nonlinear Analysis, Theory, Method Appl. 26 (1996), 1023-1033.
18. A. PAZY, Semigroups of linear operators and applications to partial differential equations (Springer, New York, 1983).