Article PDF
Avoid common mistakes on your manuscript.
References
A. Marchaud, Sur les champs des demi-droites et les équations différentielles du premier ordre,Bull. Soc. Math. France 63 (1934), 1–38.
A. Marchaud, Sur les champs continus de demi-cones convexes et leurs intégrales,Compositio Math. 3 (1936), 89–127.
S. C. Zaremba, Sur les équations au paratingent,Bull. Sci. Math. (2)60 (1936), 139–160.
T. Ważewski, Systèmes de commande et équations au contingent,Bull. Acad. Polon. Sci. 9 (1961), 151–155.
T. Ważewski, Sur une condition équivalente à l'équation au contingent,Bull. Acad. Polon. Sci. 9 (1961), 865–867.
E. Roxin, On generalized dynamical systems defined by contingent equations,J. Differential Equations 1 (1965), 188–205.
A. F. Filippov, On certain questions in the theory of optimal control,J. SIAM Control Ser. A 1 (1962), 76–84.
E. Roxin, The existence of optimal controls,Michigan Math. J. 9 (1962), 109–119.
T. F. Bridgland, Jr., andJ. S. Hinkel, The minimum miss distance problem,Proc. Amer. Math. Soc. 18 (1967), 457–464.
H. Hermes, The equivalence and approximation of optimal control problems,J. Differential Equations 1 (1965), 409–426.
T. F. Bridgland, Jr., On the problem of approximate synthesis of optimal controls,J. SIAM Control 5 (1967), 326–344;ibid. 6 (1968), 58.
P. Hartman,Ordinary Differential Equations, J. Wiley & Sons, New York, 1964.
A. F. Filippov, Differential equations with many-valued discontinuous right-hand side,Soviet Math. 4 (1963), 941–945.
T. Bonnesen andW. Fenchel,Theorie der Konvexen Körper, Chelsea Publ. Co., New York, 1948.
H. G. Eggleston,Convexity, Cambridge University Press, Cambridge, 1958.
F. A. Valentine,Convex Sets, McGraw-Hill, New York, 1964.
E. W. Hobson,The Theory of Functions of a Real Variable and the Theory of Fourier Series, Vol. II, Dover, New York, 1957.
A. E. Taylor,General Theory of Functions and Integration, Blaisdell, New York, 1965.
J. Szarski,Differential Inequalities, Polish Scientific Publishers, Warsaw, 1965.
T. F. Bridgland, Jr., A criterion for weak controllability,Math. Systems Theory 2 (1968), 51–56.
C. Castaing, Sur les équations différentielles multivoques,C. R. Acad. Sci. Paris 263 (1966), A63-A66.
E. A. Barbashin, On the theory of generalized dynamical systems,Uchen. Zapiski Moskov. Gos. Univ. No. 135 (1949), 110–133.
E. Roxin, Stability in general control systems,J. Differential Equations 1 (1965), 115–150.
P. P. Varaiya, On the existence of solutions to a differential game,J. SIAM Control 5 (1967), 153–162.
E. O. Roxin, On Varaiya's definition of a differential game,Proc. U.S.-Japan Seminar on Diff. and Functional Equations (ed. W. A. Harris, Jr., and Y. Sibuya), pp. 491–495, W. A. Benjamin Inc., New York, 1967.
Author information
Authors and Affiliations
Additional information
This research was carried out while the author was associated with the University of Alabama Research Institute. It was supported in part by the U.S. Army Missile Command under contract DA-AH01-67-C1630 and in part by a stipendiary grant from Brown Engineering Company.
Rights and permissions
About this article
Cite this article
Bridgland, T.F. Contributions to the theory of generalized differential equations. I.. Math. Systems Theory 3, 17–50 (1969). https://doi.org/10.1007/BF01695624
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01695624