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Mixed type semicontinuous differential inclusions in Banach spaces

100%

Donchev T.

2001

tom 77

nr 3

245-259

We consider a class of differential inclusions in (nonseparable) Banach spaces satisfying mixed type semicontinuity hypotheses and prove the existence of solutions for a problem with state constraints. The cases of dissipative type conditions and with time lag are also studied. These results are then applied to control systems.

Lower semicontinuous differential inclusions. One-sided Lipschitz approach

100%

Donchev T.

Colloquium Mathematicum

1997

tom 74

nr 2

177-184

Some properties of differential inclusions with lower semicontinuous right-hand side are considered. Our essential assumption is the one-sided Lipschitz condition introduced in [4]. Using the main idea of [10], we extend the well known relaxation theorem, stating that the solution set of the original problem is dense in the solution set of the relaxed one, under assumptions essentially weaker than those in the literature. Applications in optimal control are given.

On the theorem of Filippov-Pliś and some applications

32%

Donchev T. , Farkhi E.

Control and Cybernetics

2009

tom 38

nr 4A

1251-1271