Geodesic
Differential games in a Banach space on a fixed chain
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 12 (2020) no. 3, pp. 89-118

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The paper is devoted to obtaining the sufficient conditions for existence of $\varepsilon$-equilibrium in the sense of piecewise program strategies in antagonistic games associated with nonlinear non-autonomous controlled differential equation in a Banach space and cost functional of a general enough form. The concept of piecewise program strategies in such a game is defined on the base of a concept of Volterra set chain for a right-hand operator of the corresponding integral equation controlled by the opponent players and according to a given partition of the time segment. As example we consider the game associated with a nonlinear pseudoparabolic partial differential equation governing the evolution of electric field in a semiconductor.
Keywords: differential game, nonlinear differential equation in a Banach space, piecewise program strategies, $\varepsilon$-equilibrium.
Mots-clés : Volterra set chain 
@article{MGTA_2020_12_3_a3,
     author = {Andrey V. Chernov},
     title = {Differential games in a {Banach} space on a fixed chain},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {89--118},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2020_12_3_a3/}
}
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Andrey V. Chernov. Differential games in a Banach space on a fixed chain. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 12 (2020) no. 3, pp. 89-118. http://geodesic.mathdoc.fr/item/MGTA_2020_12_3_a3/