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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.

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