Weak solutions of ordinary differential equations in Banach spaces

Applied Mathematics Letters

Volumn 12, Issue 1, 1999, Pages 101-105

  O'Regan, D ^a  

^a NATIONAL UNIVERSITY OF IRELAND   (Ireland)

Author keywords

Equations in Banach spaces; Weak topology; Weakly sequentially continuous

Indexed keywords

EID: 0002061550     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(98)00133-5     Document Type: Article

References (14)

1. A. Szep, Existence theorems for weak solutions of ordinary differential equations in reflexive Banach spaces, Studia Sci. Math. Hungar. 6, 197-203 (1971).
2. E. Cramer, V. Lakshmikantham and A.R. Mitchell, On the existence of weak solutions of differential equations in nonreflexive Banach spaces, Nonlinear Anal. 2, 169-177 (1978).
3. D. Bugajewski, On the existence of weak solutions of integral equations in Banach spaces, Comment. Math. Univ. Carolinae 35, 35-41 (1994).
4. M. Cichoń, Weak solutions of differential equations in Banach spaces, Discuss. Mathematicae - Differential Inclusions 15, 5-14 (1995).
5. M. Cichoń and I. Kubiaczyk, Existence theorems for the Hammerstein integral equation, Discussiones Mathematicae - Differential Inclusions 16, 171-177 (1996).
6. A.R. Mitchell and C.K.L. Smith, An existence theorem for weak solutions of differential equations in Banach spaces, In Nonlinear Equations in Abstract Spaces, (Edited by V. Lakshmikantham), pp. 387-404, Academic Press, (1978).
7. D. O'Regan, Integral equations in reflexive Banach spaces and weak topologies, Proc. Amer. Math. Soc. 124, 607-614 (1996).
8. D. O'Regan, Fixed point theory for weakly sequentially continuous mappings, Mathl. Comput. Modelling 27 (5), 1-14 (1998).
9. D. O'Regan, Operator equations in Banach spaces relative to the weak topology, (to appear).
10. F.S. DeBlasi, On a property of the unit sphere in Banach spaces, Bull. Math. Soc. Sci. Math. Roum. 21, 259-262 (1977).
11. I. Kubiaczyk and S. Szufla, Kneser's theorem for weak solutions of ordinary differential equations in Banach spaces, Publ. Inst. Math. (Beograd) 46, 99-103 (1982).
12. C.K.L. Smith, Measure of nonconvergence and noncompactness, Ph.D Thesis, University of Texas at Arlington, (1978).
13. O. Arino, S. Gautier and J.P. Penot, A fixed point theorem for sequentially continuous mappings with applications to ordinary differential equations, Funkc. Ekvac. 27, 273-279 (1984).
14. R.F. Geitz, Pettis integration, Proc. Amer. Math. Soc. 82, 81-86 (1981).