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A majorant criterion for the total preservation of global solvability of controlled functional operator equation. (English. Russian original) Zbl 1244.47064
Russ. Math. 55, No. 3, 85-95 (2011); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2011, No. 3, 95-107 (2011).
The author formulates a nonlinear controlled functional operator equation in a Banach ideal space. The unique solvability proved by applied techniques from nonlinear functional analysis. Sufficient conditions for the global solvability of all controls from a pointwise bounded set are given. It should be noted here that the paper includes some examples which are of particular value, because the corresponding controlled value problems are reduced step by step to the considered equation for which one can obtain results applying classical techniques.

##### MSC:
 47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics 49J15 Existence theories for optimal control problems involving ordinary differential equations 39B42 Matrix and operator functional equations 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 34K30 Functional-differential equations in abstract spaces 93C25 Control/observation systems in abstract spaces
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##### References:
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