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Generalized differential equations with strongly one-sided Lipschitzian right-hand side. (English. Russian original) Zbl 0903.34015
Differ. Equations 32, No. 11, 1485-1491 (1996); translation from Differ. Uravn. 32, No. 11, 1488-1494 (1996).
The authors study differential inclusions \(\dot x(t)\in F(x(t))\) with set-valued right-hand sides satisfying a strengthened Lipschitz condition. The authors find some additional restrictions on the mapping \(F\) providing the first-order convergence of the explicit Euler scheme for a solution to the Cauchy problem for this inclusion even without the assumption that \(F\) is discontinuous with respect to the phase variables. The main results are concerned with the structure of values of strongly one-sided Lipschitzian mappings and with the determination of the set of their discontinuity points.
Seventeen references fully cover the topic.

34A60 Ordinary differential inclusions
49K24 Optimal control problems with differential inclusions (nec./ suff.) (MSC2000)
49J24 Optimal control problems with differential inclusions (existence) (MSC2000)