Skip to main content
Log in

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Attouch H,Variational Convergence for Functional and Operators (London: Pitman) (1984)

    Google Scholar 

  2. Aubin J -P and Cellina A,Differential Inclusions (Berlin: Springer) (1983)

    Google Scholar 

  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. 1–23

    Article  MATH  MathSciNet  Google Scholar 

  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. 745–767

    MATH  MathSciNet  Google Scholar 

  5. Bressan A, On differential relations with lower semicontinuous right hand side,J. Differ. Equ. 37 (1980) pp. 89–97

    Article  MATH  MathSciNet  Google Scholar 

  6. Brezis H,Operateurs Maximaux Monotones (Amsterdam: North Holland) (1973)

    MATH  Google Scholar 

  7. Cellina A and Marchi M, Nonconvex perturbations of maximal monotone differential inclusions,Israel J. Math. 46 (1983) pp. 1–11

    Article  MATH  MathSciNet  Google Scholar 

  8. Dunford N and Schwartz J,Linear Operators I (New York: Wiley) (1958)

    MATH  Google Scholar 

  9. Fryszkowski A, Continuous selections for a class of nonconvex multivalued maps,Stud. Math. 76 (1983) pp. 163–174

    MATH  MathSciNet  Google Scholar 

  10. Henry C, Differential equations with discontinuous right hand side for planning procedures,J. Econ. Theory 4 (1972) pp. 545–551

    Article  MathSciNet  Google Scholar 

  11. Kandilakis D and Papageorgiou N S, Nonsmooth analysis and approximation,J. Approx. Theory 52 (1988) pp. 58–81

    Article  MATH  MathSciNet  Google Scholar 

  12. Klein E and Thompson A,Theory of Correspondences (New York: Wiley) (1984)

    MATH  Google Scholar 

  13. Kuratowski K,Topology I (New York; Academic Press) (1966)

    Google Scholar 

  14. Moreau J -J, Evolution problem associated with a moving convex set in a Hilbert space,J. Differ. Equ. 26 (1977) pp. 347–374

    Article  MATH  MathSciNet  Google Scholar 

  15. Mosco U, Convergence of convex sets and solutions of variational inequalities,Adv. Math. 3 (1969) pp. 510–585

    Article  MATH  MathSciNet  Google Scholar 

  16. Papageorgiou N S, Convergence theorems for Banach space valued integrable multifunctions,Int. J. Math. Math. Sci. 10 (1987) pp. 433–442

    Article  MATH  Google Scholar 

  17. Papageorgiou N S, Measurable multifunctions and their applications to convex integral functionals,Int. J. Math. Math. Sci. 12 (1989) pp. 175–192

    Article  MATH  Google Scholar 

  18. Stacchetti E, Analysis of a dynamic, decentralized exchange economy,J. Math. Econ. 14 (1985) pp. 241–259

    Article  MathSciNet  Google Scholar 

  19. Vrabie I,Compactness Methods in Nonlinear Evolutions (Essex: Longman) (1987)

    Google Scholar 

  20. Wagner D, Survey of measurable selection theorems,SIAM J. Control Optim. 15 (1977) pp. 859–903

    Article  MATH  Google Scholar 

  21. Warga J,Optimal Control of Differential and Functional Equations (New York: Academic Press) (1970)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Papageorgiou, N.S. Maximal monotone differential inclusions with memory. Proc. Indian Acad. Sci. (Math. Sci.) 102, 59–71 (1992). https://doi.org/10.1007/BF02837180

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02837180

Keywords

Navigation