Advertisement

Maximal monotone differential inclusions with memory

  • Nikolaos S. Papageorgiou
Article
  • 39 Downloads

Abstract

In this paper we study maximal monotone differential inclusions with memory. First we establish two existence theorems; one involving convex-valued orientor fields and the other nonconvex valued ones. Then we examine the dependence of the solution set on the data that determine it. Finally we prove a relaxation theorem.

Keywords

Maximal monotone operator resolvent resolvent convergence topology selection theorem relaxation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Attouch H,Variational Convergence for Functional and Operators (London: Pitman) (1984)Google Scholar
  2. [2]
    Aubin J -P and Cellina A,Differential Inclusions (Berlin: Springer) (1983)Google Scholar
  3. [3]
    Avgerinos E and Papageorgiou N S, On the sensitivity and relaxability of optimal control problems governed by nonlinear evolution equations with state constraints,Monatsh. Math. 109 (1990) pp. 1–23MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Avgerinos E and Papageorgiou N S, Optimal control and relaxation for a class of nonlinear distributed parameter systems,Osaka J. Math. 27 (1990) pp. 745–767MATHMathSciNetGoogle Scholar
  5. [5]
    Bressan A, On differential relations with lower semicontinuous right hand side,J. Differ. Equ. 37 (1980) pp. 89–97MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Brezis H,Operateurs Maximaux Monotones (Amsterdam: North Holland) (1973)MATHGoogle Scholar
  7. [7]
    Cellina A and Marchi M, Nonconvex perturbations of maximal monotone differential inclusions,Israel J. Math. 46 (1983) pp. 1–11MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Dunford N and Schwartz J,Linear Operators I (New York: Wiley) (1958)MATHGoogle Scholar
  9. [9]
    Fryszkowski A, Continuous selections for a class of nonconvex multivalued maps,Stud. Math. 76 (1983) pp. 163–174MATHMathSciNetGoogle Scholar
  10. [10]
    Henry C, Differential equations with discontinuous right hand side for planning procedures,J. Econ. Theory 4 (1972) pp. 545–551CrossRefMathSciNetGoogle Scholar
  11. [11]
    Kandilakis D and Papageorgiou N S, Nonsmooth analysis and approximation,J. Approx. Theory 52 (1988) pp. 58–81MATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    Klein E and Thompson A,Theory of Correspondences (New York: Wiley) (1984)MATHGoogle Scholar
  13. [13]
    Kuratowski K,Topology I (New York; Academic Press) (1966)Google Scholar
  14. [14]
    Moreau J -J, Evolution problem associated with a moving convex set in a Hilbert space,J. Differ. Equ. 26 (1977) pp. 347–374MATHCrossRefMathSciNetGoogle Scholar
  15. [15]
    Mosco U, Convergence of convex sets and solutions of variational inequalities,Adv. Math. 3 (1969) pp. 510–585MATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    Papageorgiou N S, Convergence theorems for Banach space valued integrable multifunctions,Int. J. Math. Math. Sci. 10 (1987) pp. 433–442MATHCrossRefGoogle Scholar
  17. [17]
    Papageorgiou N S, Measurable multifunctions and their applications to convex integral functionals,Int. J. Math. Math. Sci. 12 (1989) pp. 175–192MATHCrossRefGoogle Scholar
  18. [18]
    Stacchetti E, Analysis of a dynamic, decentralized exchange economy,J. Math. Econ. 14 (1985) pp. 241–259CrossRefMathSciNetGoogle Scholar
  19. [19]
    Vrabie I,Compactness Methods in Nonlinear Evolutions (Essex: Longman) (1987)Google Scholar
  20. [20]
    Wagner D, Survey of measurable selection theorems,SIAM J. Control Optim. 15 (1977) pp. 859–903MATHCrossRefGoogle Scholar
  21. [21]
    Warga J,Optimal Control of Differential and Functional Equations (New York: Academic Press) (1970)Google Scholar

Copyright information

© Indian Academy of Sciences 1992

Authors and Affiliations

  • Nikolaos S. Papageorgiou
    • 1
    • 2
  1. 1.Department of Applied MathematicsFlorida Institute of TechnologyMelbourneUSA
  2. 2.Department of MathematicsNational Technical UniversityAthensGreece

Personalised recommendations