Stone-Čech compactification with applications to evolution equations on Banach spaces

Publicationes Mathematicae Debrecen

Volumn 59, Issue 3-4, 2001, Pages 289-301

  Ahmed, N U ^a  

^a UNIVERSITY OF OTTAWA   (Canada)

Author keywords

Evolution equations; Finitely additive measures; Measure solutions; Stone ech compactification

Indexed keywords

EID: 4544275484     PISSN: 00333883     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (16)

1. S. WILLARD, General Topology, Addison-Wesley Publishing Company, Reading, Massachusetts, Menlo park, California, London, Don Mills, Ontario, 1970.
2. N. U. AHMED, Measure solutions for semilinear systems with unbounded nonlinearities, Nonlinear Analysis: Theory Methods and Applications 35 (1998), 487-503.
3. N. U. AHMED, Semigroup Theory with Applications to Systems and Control, Pitman Res. Notes in Math. Ser., 246, Longman Scientific and Technical and John Wiley, London, New York, 1991.
4. N. U. AHMED, Measure solutions for semilinear evolution equations with polynomial growth and their optimal controls, Discussiones Mathematicae: Differential Inclusions 17 (1997), 5-27.
5. H. O. FATTORINI, A remark on existence of solutions of infinite dimensional non-compact optimal control problems, SIAM J. Contr. and Optim. 35, 4 (1996), 1422-1433.
6. N. U. AHMED, Relaxed solutions for stochastic evolution equations on Hilbert space with polynomial nonlinearities, Publ. Math. Debrecen 54 (1999), 75-101.
7. N. DUNFORD and J. T. SCHWARTZ, Linear Operators, Part 1, Interscience Publishers, Inc., New York, 1958.
8. A. N. GODUNOV, Peano's theorem in infinite dimensional Hilbert space is false even in a weakened formulation, Math. Zametki 15 (1974), 467-477.
9. A. I. TULCEA and C. I. TULCEA, Topics in the Theory of Lifting, Springer-Verlag, Berlin, Heidelberg, New York, 1969.
10. S. SALBANY and T. TODOROV, Nonstandard Analysis in Point-Set Topology, E. Schrödinger International Institute for Mathematical Physics, Vienna, 1999, (preprint ESI 666).
11. M. OBERGUGGENBERGER, Contributions of nonstandard analysis to partial differential equations, in: Developments in Nonstandard Mathematics (N. J. Cutland, V. Neves, F. Oliveira and J. Sousa-Pinto, eds.), Longman Press, Harlow, 1995, 130-150.
12. T. TODOROV, An existence result for a class of partial differential equations with smooth coefficients, in: Advances in Analysis, Probability and Mathematical Physics Contributions to Nonstandard Analysis (S. Albeverio, W. A. Luxemburg and M. P. H. Wolf, eds.), Vol. 314, Kluwer Acad. Publ., Dordrecht, 1995, 107-121.
13. ∞-coefficients in an algebra of generalized functions, in Transactions of the American Mathematical Society 348, 2 (1996), 673-689.
14. S. SALBANY and T. TODOROV, Nonstandard and Standard Compactifications, Journal of Symbolic Logic 65, 4 (2000), 1836-1840.
15. N. U. AHMED, Measure solutions for semilinear and quasilinear evolution equations and their optimal control, Nonlinear Analysis 40 (2000), 51-72.
16. N. U. AHMED, A general result on measure solutions for semilinear evolution equations, Nonlinear Analysis 42 (2000), 1335-1349.