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Cauchy problems for certain Isaacs-Bellman equations and games of survival. (English) Zbl 0302.90074


MSC:

91A23 Differential games (aspects of game theory)
91A05 2-person games
31-XX Potential theory
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References:

[1] Robert J. Elliott and Nigel J. Kalton, Values in differential games, Bull. Amer. Math. Soc. 78 (1972), 427 – 431. · Zbl 0253.90074
[2] Robert J. Elliott and Nigel J. Kalton, The existence of value in differential games, American Mathematical Society, Providence, R.I., 1972. Memoirs of the American Mathematical Society, No. 126. · Zbl 0244.90046
[3] Robert J. Elliott and Nigel J. Kalton, The existence of value in differential games of pursuit and evasion, J. Differential Equations 12 (1972), 504 – 523. · Zbl 0244.90046
[4] Avner Friedman, Differential games, Wiley-Interscience [A division of John Wiley & Sons, Inc.], New York-London, 1971. Pure and Applied Mathematics, Vol. XXV. · Zbl 0229.90060
[5] Avner Friedman, Comparison theorems for differential games. I, II, J. Differential Equations 12 (1972), 162 – 172; ibid. 12 (1972), 396 – 416. · Zbl 0224.90083
[6] Paul R. Halmos, Measure Theory, D. Van Nostrand Company, Inc., New York, N. Y., 1950. · Zbl 0040.16802
[7] John G. Hocking and Gail S. Young, Topology, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1961. · Zbl 0718.55001
[8] Rufus Isaacs, Differential games. A mathematical theory with applications to warfare and pursuit, control and optimization, John Wiley & Sons, Inc., New York-London-Sydney, 1965. · Zbl 0125.38001
[9] M. Krzyzański, Partial differential equations of second order. Vol. 1, Monografie Mat., Tom 53, PWN, Warsaw, 1957; English transl., PWN, Warsaw, 1971. MR 20 #6576; MR 43 #3597.
[10] Oskar Perron, Eine neue Behandlung der ersten Randwertaufgabe für \Delta \?=0, Math. Z. 18 (1923), no. 1, 42 – 54 (German). · JFM 49.0340.01
[11] A. N. V. Rao, Comparison of differential games of fixed duration, SIAM J. Control 10 (1972), 393 – 397. · Zbl 0252.90062
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