Measure solutions for evolution equations with discontinuous vector fields and their optimal control

Nonlinear Analysis, Theory, Methods and Applications

Volumn 63, Issue 5-7, 2005, Pages

  Ahmed, N U ^a  

^a UNIVERSITY OF OTTAWA   (Canada)

Author keywords

Discontinuous vector fields; Measure solutions; Optimal control

Indexed keywords

OPTIMAL CONTROL SYSTEMS; VECTORS;

DISCONTINUOUS VECTOR FIELDS; MEASURE SOLUTIONS;

DIFFERENTIAL EQUATIONS;

EID: 28044446347     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.12.027     Document Type: Conference Paper

References (24)

1. R.P. Agarwall, and S.G. Leela A brief biography and survey of collected works of V. Lakshmikantham Nonlinear Anal. 40 2000 1 19
2. N.U. Ahmed, Semigroup theory with applications to systems and control, Pitman Research Notes in Mathematics Series, vol. 246, Longman Scientific and Technical, UK, Co-published with Wiley, New York, USA, 1991.
3. N.U. Ahmed Measure solutions for semilinear evolution equations with polynomial growth and their optimal control Discuss. Math. Differential Inclusions 17 1997 5 27
4. N.U. Ahmed Measure solutions for impulsive systems in Banach spaces and their control Dyn. Contin. Discrete Impulsive Systems 6 1999 519 535
5. N.U. Ahmed Relaxed solutions for stochastic evolution equations on Hilbert space with polynomial nonlinearities Publ. Math. Debrecen 54 1999 75 101
6. N.U. Ahmed Optimal impulse control for impulsive systems in Banach spaces International J. Differential Equations Appl. 1 1 2000 37 52
7. N.U. Ahmed Measure solutions for semilinear and quasilinear evolution equations and their optimal control Nonlinear Anal. 40 2000 51 72
8. N.U. Ahmed A general result on measure solutions for semilinear evolution equations Nonlinear Anal. 42 2000 1335 1349
9. N.U. Ahmed Some remarks on the dynamics of impulsive systems in Banach spaces Dyn. Contin. Discrete Impulsive Systems 8 2001 261 274
10. N.U. Ahmed Systems governed by impulsive differential inclusions on Hilbert spaces Nonlinear Anal. 45 2001 693 706
11. N.U. Ahmed Measure solutions impulsive evolutions differential inclusions and optimal control Nonlinear Anal. 47 2001 13 23
12. 0-semigroups and evolution inclusions Nonlinear Funct. Anal. Appl. 7 4 2002 555 580
13. N.U. Ahmed Impulsive evolution equations in infinite dimensional spaces Dyn. Contin. Discrete Impulsive Systems Ser. A 10 2003 11 24
14. N.U. Ahmed Existence of optimal controls for a general class of impulsive systems on Banach spaces SIAM J. Control Optim. 42 2 2003 669 685
15. 0-semigroups by operator valued measures Nonlinear Funct. Anal. Appl. 9 1 2004 127 147
16. N.U. Ahmed Measure solutions for evolution equations with discontinuous vector fields Nonlinear Funct. Anal. Appl. 9 3 2004 467 484
17. N.U. Ahmed Optimal control for evolution equations with discontinuous vector fields Dyn. Contin. Discrete Impulsive Systems Ser. A 11 2004 105 118
18. N.U. Ahmed, Measure solutions for impulsive evolution equations with measurable vector fields (JMAA), submitted.
19. N.U. Ahmed, Necessary conditions of optimality for evolution equations with discontinuous vector fields, Nonlinear Funct. Anal. Appl., to appear.
20. N.U. Ahmed, K.L. Teo, and S.H. Hou Nonlinear impulsive systems on infinite dimensional spaces Nonlinear Anal. 54 2003 907 925
21. H.O. Fattorini, A remark on existence of solutions of infinite dimensional noncompact optimal control problems 35(4) (1997) 1422-1433.
22. A.N. Godunov Peano's theorem in infinite dimensional Hilbert S is false even in a weakened formulation Math. Zametki 15 1974 75 101
23. V. Lakshmikantham, D.D. Bainov, and P.S. Simeonov Theory of Impulsive Differential Equations 1989 World Scientific Singapore, London
24. J.H. Liu Nonlinear impulsive evolution equations Dyn. Contin. Discrete Impulsive Systems 6 1 1999 77 85