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Nonlinear set-valued boundary value problems with continuous feedback

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Abstract

We obtain sufficient conditions for the existence of at least one absolutely continuous solution of a nonlinear functional-differential inclusion in a finite-dimensional space with nonlinear set-valued functional boundary conditions. The set-valuedness of the dynamics may be due to the presence of a control. In addition, we consider the case in which the set-valuedness of the system dynamics and the boundary conditions is specified by inequalities. We assume the presence of a continuous feedback and impose the requirements of solvability of the open-loop problem. Statements of problems of this type arise in connection with the analysis of conflict-control systems.

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Authors and Affiliations

  1. Institute for Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia

    S. A. Brykalov

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  1. S. A. Brykalov
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Correspondence to S. A. Brykalov.

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Original Russian Text © S.A. Brykalov, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 2, pp. 167–174.

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Brykalov, S.A. Nonlinear set-valued boundary value problems with continuous feedback. Diff Equat 50, 169–176 (2014). https://doi.org/10.1134/S0012266114020049

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  • DOI: https://doi.org/10.1134/S0012266114020049

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