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On contingent equations

Section I

Part of the Lecture Notes in Mathematics book series (LNM,volume 243)

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References

  1. Aumann, R. J., Integrals of set values functions, J. Math. Anal. and Appl. 12 (1965), 1–12.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Castaing, Ch., Sur les équations différentielles multivoques, C. R. Acad. Sc. Paris, t.263 (1966), 63–66.

    MathSciNet  MATH  Google Scholar 

  3. Filippov, A. F., On certain questions in the theory of optimal control, J. SIAM Control, 1 (1962), 76–84.

    MathSciNet  MATH  Google Scholar 

  4. _____, Differential equations with many-valued discontinuous right-hand side, Soviet Math. Dokl., 4 (1963), 941–945.

    MATH  Google Scholar 

  5. _____, Classical solutions of differential equations with multivalued right-hand side, SIAM J. Control, 5 (1967), 609–621.

    CrossRef  MathSciNet  Google Scholar 

  6. Hermes, H., A note on the range of a vector measure; applications to the theory of optimal control, J. Math. Anal. and Appl., 8 (1964), 78–83.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. _____, Calculus of set valued functions and control, J. Math. and Mech., 18 (1968), 47–59.

    MathSciNet  MATH  Google Scholar 

  8. _____, The generalized differential equation x ɛ R(t,x), Advances in Mathematics, 4 (1970), 149–169.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Hukuhara, M., Sur les systèmes d'équations différentielles ordinaires, Jap. Journ. of Math. 6 (1930), 269–299.

    Google Scholar 

  10. __, Sur l'application semi-continue dont la valeur est un compact convexe, RIMS-11, Res. Inst. Math. Sci., Kyoto Univ., (1966).

    Google Scholar 

  11. __, Intégration des applications mesurables dont la valeur est un compact convexe, RIMS-15, Res. Inst. Math. Sci., Kyoto Univ., (1966).

    Google Scholar 

  12. Kikuchi, N., Existence of optimal controls, RIMS-20, Res. Inst. Math. Sci., Kyoto Univ., (1967).

    Google Scholar 

  13. _____, Control problems of contingent equation, Publ. RIMS, Kyoto Univ. Ser. A, 3 (1967), 85–99.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. _____, On some fundamental theorems of contingent equations in connection with the control problems, Publ. RIMS, Kyoto Univ. Ser. A, 3 (1967), 177–201.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. _____, On contingent equations satisfying the Carathéodory type conditions, Publ. RIMS, Kyoto Univ. Ser. A, 3 (1967), 361–371.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. _____, On contingent equations and control problems, Funkcial. Ekvac. (Japanese) I, II, 21 (1969), 3–43; 22(1969), 1–24.

    Google Scholar 

  17. _____, On control problems for functional-differential equations, Funkcial. Ekvac. 14 (1971), 1–23.

    MathSciNet  MATH  Google Scholar 

  18. LaSalle, J. P., The time optimal control problem, Contr. Theory Nonlinear Oscillations (Princeton), 5 (1961), 1–24.

    MATH  Google Scholar 

  19. Marchaud, A., Sur les champs des demi-droites et les équations différentielles du premier ordre, Bull. Soc. Math. France 63 (1934), 1–38.

    MathSciNet  MATH  Google Scholar 

  20. _____, Sur les champs continus de demi-cônes convexes et leurs intégrales, Compositio Math. 3 (1936), 89–127.

    MathSciNet  MATH  Google Scholar 

  21. Pliś, A., Remarks on measurable set-valued functions, Bull. Acad. Polon. Sci., 9 (1961), 857–859.

    MathSciNet  MATH  Google Scholar 

  22. _____, Measurable orientor fields, Bull. Acad. Polon. Sci., 13 (1965), 565–569.

    MathSciNet  MATH  Google Scholar 

  23. Pontryagin, L. S., et al., The mathematical theory of optimal processes, Interscience, New York, 1962.

    MATH  Google Scholar 

  24. Scorza-Oragoni, G., Un teorem sulle funzioni continue rispetto ad une e misurabili rispetto ad un altra variable, Rend. Sem. Mat. Univ. Padova, 17 (1948), 102–106.

    MathSciNet  MATH  Google Scholar 

  25. Ważewski, T., Systèmes de commande et équations au contingent, Bull. Acad. Polon. Sci., 9 (1961), 151–155.

    MATH  Google Scholar 

  26. _____, Sur une condition d'existence des functions implicites measurables, Bull. Acad. Polon. Sci., 9 (1961), 861–863.

    MATH  Google Scholar 

  27. ________, Sur une condition équivalent à l'équation au contingent, Bull. Acad. Polon. Sci., 9 (1961), 865–867.

    MATH  Google Scholar 

  28. ________, Sur la sémicontinuité inférieure du "tendeur" d'un ensemble compact, variant d'un façon continue, Bull. Acad. Polon. Sci., 9 (1961), 869–872.

    MATH  Google Scholar 

  29. ________, Sur une généralisation de la notion des solution d'une équation au contingent, Bull. Acad. Polon. Sci., 10 (1962), 11–15.

    MATH  Google Scholar 

  30. ________, Sur les systèmes de commande non linéaires dont le contredomaine de commande n'est pas forcément convexe, Bull. Acad. Polon. Sci., 10 (1962), 17–21.

    MATH  Google Scholar 

  31. ________, Sur quelques définitions équivalentes des quasitrajectoires des systèmes de commande, Bull. Acad. Polon. Sci., 10 (1962), 469–474.

    MATH  Google Scholar 

  32. __, On an optimal control problem, Differential Equations and Their Applications: Proceeding of the Conference held in Prague, September 1962 (1963), 229–242.

    Google Scholar 

  33. Zaremba, S. C., Sur les équations au paratingent, Bull. Sci. Math. (12) 60 (1936), 139–160.

    MATH  Google Scholar 

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© 1971 Springer-Verlag

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Kikuchi, N. (1971). On contingent equations. In: Urabe, M. (eds) Japan-United States Seminar on Ordinary Differential and Functional Equations. Lecture Notes in Mathematics, vol 243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058726

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  • DOI: https://doi.org/10.1007/BFb0058726

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