On the approximate K-controllability of nonlinear systems in Banach spaces

Nonlinear Analysis, Theory, Methods and Applications

Volumn 62, Issue 2, 2005, Pages 315-344

  Kartsatos, Athanassios G ^a  

^a UNIVERSITY OF SOUTH FLORIDA   (United States)

Author keywords

Approximate K controllability; Evans solutions; Evolution operators; Kato solutions; m Accretive operators; Mild solutions; Preassigned responses

Indexed keywords

BOUNDARY CONDITIONS; CONTROLLABILITY; FUNCTIONS; MAPPING; MATHEMATICAL OPERATORS; PARTIAL DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; SET THEORY;

APPROXIMATE K-CONTROLLABILITY; EVANS-SOLUTIONS; EVOLUTION OPERATORS; KATO-SOLUTIONS; M-ACCRETIVE OPERATORS; MILD-SOLUTIONS; PREASSIGNED RESPONSES;

NONLINEAR SYSTEMS;

EID: 18944391168     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2005.02.118     Document Type: Article

References (31)

1. K. Balachandran, and J.P. Dauer Controllability of nonlinear systems in Banach spaces: a survey J. Optim. Theory Appl. 115 2002 7 28
2. V. Barbu Nonlinear Semigroups and Differential Equations in Banach Spaces 1975 Noordhoff International Publishing Leyden, The Netherlands
3. W.M. Bian Controllability of nonlinear evolution systems with preassigned responses J. Optim. Theory Appl. 100 1999 265 285
4. F. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proc. Symp. Pure Appl. Math. 18, Part 2, Providence, 1976.
5. I. Cioranescu Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems 1990 Kluwer Academic Publishers Boston
6. L.C. Evans Nonlinear evolution equations in an arbitrary Banach space Israel J. Math. 26 1977 1 42
7. W.E. Fitzgibbon Nonlinear perturbations of linear evolution equations in a Banach space Ann. Mat. Pura Appl. 110 1976 279 293
8. A. Friedman Partial Differential Equations 1969 Holt, Rinehart and Winston New York
9. Z. Guan, and A.G. Kartsatos Ranges of perturbed maximal monotone and m -accretive operators in Banach spaces Trans. Amer. Math. Soc. 347 1995 2403 2435
10. D.R. Kaplan, and A.G. Kartsatos Ranges of sums and control of nonlinear evolutions with preassigned responses J. Optim. Theory Appl. 81 1994 121 141
11. A.G. Kartsatos Advanced Ordinary Differential Equations 1993 Mancorp Publishing Inc. Tampa, FL
12. A.G. Kartsatos, Recent results involving compact perturbations and compact resolvents of accretive operators in Banach spaces, Proceedings of the First World Congress of Nonlinear Analysts, Tampa, FL, 1992, vol. III, 1995, Walter De Gruyter, New York, pp. 2197-2222.
13. A.G. Kartsatos A compact evolution operator generated by a time-dependent m -accretive operator in a general Banach space Math. Ann. 302 1995 473 487
14. A.G. Kartsatos New results in the perturbation theory of maximal monotone and m -accretive operators in Banach spaces Trans. Amer. Math. Soc. 348 1996 1663 1707
15. A.G. Kartsatos, and C. Liang Extending the class of pre-assigned responses in problems of K -controllability in general Banach spaces Nonlinear Analysis TMA 28 1997 235 245
16. A.G. Kartsatos, and J. Lin Homotopy invariance of parameter-dependent domains and perturbation theory for maximal monotone and m -accretive operators in Banach spaces Adv. Differential Equations 8 2003 129 160
17. A.G. Kartsatos, and R.D. Mabry Controlling the space with pre-assigned responses J. Optim. Theory Appl. 54 1987 517 540
18. A.G. Kartsatosm, and M.E. Parrott The weak solution of a functional differential equation in a general Banach space J. Differential Equations 75 1988 290 302
19. A.G. Kartsatos, and K.-Y. Shin Solvability of functional evolutions via compactness methods in general Banach spaces Nonlinear Analysis TMA 21 1993 517 535
20. A.G. Kartsatos, and I.V. Skrypnik Normalized eigenvectors for nonlinear abstract and elliptic operators J. Differential Equations 155 1999 443 475
21. A.G. Kartsatos, and I.V. Skrypnik Topological degree theories for densely defined mappings involving operators of type (S +) Adv. Differential Equations 4 1999 413 456
22. A.G. Kartsatos, I.V. Skrypnik, On the eigenvalue problem for perturbed nonlinear maximal monotone operators in reflexive Banach spaces, Trans. Amer. Math. Soc. 2005, to appear.
23. T. Kato Nonlinear semigroups and evolution equations J. Math. Soc. Japan 19 1967 508 520
24. V. Lakshmikantham, and S. Leela Nonlinear Differential Equations in Abstract Spaces 1981 Pergamon Press Oxford
25. N.G. Lloyd Degree Theory 1978 Cambridge University Press Cambridge
26. R.D. Mabry, Nonlinear analysis and the control of space with pre-assigned responses, Doctoral Dissertation, University of South Florida, Tampa, FL, 1985.
27. A. Pazy Semigroups of linear operators and applications to partial differential equations 1987 Springer New York
28. K. Sato On the generation of non-negative contraction semi-groups in Banach lattices J. Math. Soc. Japan 20 1968 421 436
29. I.V. Skrypnik, Methods for analysis of nonlinear elliptic boundary value problems, Transl. Math. Monographs, vol. 139, A.M.S., Providence, RI, 1994.
30. H. Tanabe Equations of Evolution 1979 Pitman London
31. A.E. Taylor Introduction to Functional Analysis 1967 Wiley New York