Global solutions for abstract functional differential equations with nonlocal conditions

Electronic Journal of Qualitative Theory of Differential Equations

Volumn , Issue , 2009, Pages 1-8

  Eduardo Hernandez, M ^a   Tanaka Aki, Sueli M ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Abstract cauchy problem; Semigroup of linear operators

Indexed keywords

EID: 85086420606     PISSN: None     EISSN: 14173875     Source Type: Journal    
DOI: 10.14232/ejqtde.2009.1.50     Document Type: Article

References (17)

1. L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (2) 494-505 (1991).
2. L. Byszewski, Existence, uniqueness and asymptotic stability of solutions of abstract nonlocal Cauchy problems, Dynam. Systems Appl. 5 (4) 595-605 (1996).
3. L. Byszewski and H. Akca, Existence of solutions of a semilinear functional differential evolution nonlocal problem, Nonlinear Anal. 34 (1) 65-72 (1998).
4. L. Byszewski and H. Akca, On a mild solution of a semilinear functional-differential evolution nonlocal problem, J. Appl. Math. Stochastic Anal. 10 (3) 265-271 (1997).
5. S. K. Ntouyas and P. Tsamatos, Global existence for semilinear evolution equations with nonlocal conditions, J.Math. Anal. Appl. 210 679-687 (1997).
6. G. L. Karakostas and P. Ch. Tsamatos, Sufficient conditions for the existence of nonnegative solutions of a nonlocal boundary value problem, Appl. Math. Lett. 15 (4) 401-407 (2002).
7. W. E. Olmstead and C. A. Roberts, The one-dimensional heat equation with a nonlocal initial condition, Appl. Math. Lett. 10 (3) 89-94 (1997).
8. E. Hernöindez, Existence results for partial neutral functional differential equations with nonlocal conditions, Dynam. Systems Appl. 11 (2) 241-252 (2002).
9. K. Balachandran, J. Y. Park and M. Chandrasekaran, Nonlocal Cauchy problem for delay integrodifferential equations of Sobolev type in Banach spaces, Appl. Math. Lett. 15 (7) 845-854 (2002).
10. Y. Hino, S. Murakami and T. Naito, In Functional-differential equations with infinite delay, Lecture Notes in Mathematics, 1473, Springer-Verlag, Berlin (1991).
11. A. Granas and J. Dugundji, Fixed Point Theory, Springer-Verlag, New York (2003).
12. E. Hernandez and M. McKibben, Some comments on: "Existence of solutions of abstract nonlinear second-order neutral functional integrodifferential equations" Comput. Math. Appl. 50 (5-6) 655-669 (2005).
13. R. H. Martin, Nonlinear Operators and Differential Equations in Banach Spaces, Robert E. Krieger Publ. Co., Florida (1987).
14. S. Aizicovici and H. Lee, Nonlinear nonlocal Cauchy problems in Banach spaces, Appl. Math. Lett. 18 (4) 401-407 (2005).
15. D. Bahuguna, Existence, uniqueness and regularity of solutions to semilinear nonlocal functional differential problems, Nonlinear Anal. 57 (7-8) 1021-1028 (2004).
16. 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. Anal. 40 (1) 11-19 (1991).
17. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, 44, Springer-Verlag, New York-Berlin (1983).