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Continuity of the non-convex play operator in the space of rectifiable curves

Jana Kopfová, Vincenzo Recupero (2023)

Applications of Mathematics

We prove that the vector play operator with a uniformly prox-regular characteristic set of constraints is continuous with respect to the $B V$ -norm and to the $B V$ -strict metric in the space of rectifiable curves, i.e., in the space of continuous functions of bounded variation. We do not assume any further regularity of the characteristic set. We also prove that the non-convex play operator is rate independent.

Continuous dependence on data for quasiautonomous nonlinear boundary value problems.

Apreutesei, N. (2005)

Abstract and Applied Analysis

Continuous selections of set of mild solutions of evolution inclusions.

Anguraj, Annamalai, Murugesan, Chinnagounder (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Continuous selections of solution sets to Volterra integral inclusions in Banach spaces.

Aizicovici, Sergiu, Staicu, Vasile (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Controllability for impulsive semilinear functional differential inclusions with a non-compact evolution operator

Irene Benedetti, Valeri Obukhovskii, Pietro Zecca (2011)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We study a controllability problem for a system governed by a semilinear functional differential inclusion in a Banach space in the presence of impulse effects and delay. Assuming a regularity of the multivalued non-linearity in terms of the Hausdorff measure of noncompactness we do not require the compactness of the evolution operator generated by the linear part of inclusion. We find existence results for mild solutions of this problem under various growth conditions on the nonlinear part and...