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Generalization of the main equation of differential game theory. (English) Zbl 0517.90100

MSC:
91A23 Differential games (aspects of game theory)
91A99 Game theory
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[1] Isaacs, R.,Differential Games, John Wiley and Sons, New York, New York, 1965.
[2] Kruzhkov, S. N.,The Cauchy Problem in the Large for Certain Quasilinear Systems of First Order with Several Variables, Doklady Akademii Nauk SSSR, Vol. 155, pp. 743-746, 1964 (in Russian).
[3] Fleming, W. H.,The Cauchy Problem for a Nonlinear First-Order Partial Differential Equation, Journal of Differential Equations, Vol. 5, pp. 515-530, 1969. · Zbl 0172.13901 · doi:10.1016/0022-0396(69)90091-6
[4] Friedman, A.,Differential Games, John Wiley and Sons (Interscience Publishers), New York, New York, 1971. · Zbl 0229.90060
[5] Krasovskii, N. N., andSubbotin, A. I.,Positional Differential Games, Nauka, Moscow, 1974 (in Russian).
[6] Subbotin, A. I., andChentzov, A. G.,Optimization of Guaranteed Result in Control Problems, Nauka, Moscow, 1981 (in Russian).
[7] Blaquiere, A., Gerard, F., andLeitmann, G.,Quantitative and Qualitative Games, Academic Press, New York, New York, 1969.
[8] Elliott, R. J., andKalton, N. J.,The Existence of Value in Differential Games of Pursuit and Evasion, Journal of Differential Equations, Vol. 12, pp. 504-523, 1972. · Zbl 0244.90046 · doi:10.1016/0022-0396(72)90022-8
[9] Fleming, W. H.,The Convergence Problem for Differential Games, Journal of Mathematical Analysis and Applications, Vol. 3, pp. 102-116, 1961. · Zbl 0113.14705 · doi:10.1016/0022-247X(61)90009-9
[10] Petrov, N. N.,On the Existence of Value for Pursuit Games, Doklady Akademii Nauk SSSR, Vol. 190, pp. 1289-1291, 1980 (in Russian).
[11] Pontryagin, L. S.,Linear Differential Games, 2, Doklady Adademii Nauk SSSR, Vol. 175, pp. 764-766, 1967 (in Russian). · Zbl 0214.40403
[12] Pshenichnii, B. N.,The Structure of Differential Games, Doklady Akademii Nauk SSSR, Vol. 184, pp. 285-287, 1969 (in Russian).
[13] Roxin, E. O.,The Axiomatic Approach in Differential Games, Journal of Optimization Theory and Applications, Vol. 3, pp. 153-163, 1969. · Zbl 0175.10504 · doi:10.1007/BF00929440
[14] Varaiya, P., andLin, J.,Existence of Saddle Points in Differential Games, SIAM Journal on Control, Vol. 7, pp. 141-157, 1969. · Zbl 0192.52402 · doi:10.1137/0307011
[15] Rademacher, H.,Über Partielle und Totale Differenzierbarkeit von Funkionen Mehrer Variablen und die Transformation der Doppelintegrale, Mathematische Annalen, Vol. 79, pp. 340-354, 1918. · JFM 47.0243.01 · doi:10.1007/BF01498415
[16] Dem’janov, V. F.,Minimax: Directional Differentiability, Izdatelstvo Leningradskogo Universiteta, Leningrad, USSR, 1974 (in Russian).
[17] Subbotin, A. I., andSubbotina, N. N.,Necessary and Sufficient Conditions for a Piecewise Smooth Value of a Differential Game, Doklady Akademii Nauk SSSR, Vol. 243, pp. 262-265, 1978 (in Russian).
[18] Janin, R.,On Sensitivity in an Optimal Control Problem, Journal of Mathematical Analysis and Applications, Vol. 60, pp. 631-657, 1977. · Zbl 0374.49012 · doi:10.1016/0022-247X(77)90006-3
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