Upper semicontinuity of Nemytskij operators
Copyright policy )Upper semicontinuity of Nemytskij operators
The authors give a growth condition on a multivalued nonlinear function \(G=G(\lambda,u)\), under which the upper semicontinuity of the function \(G(\lambda,\cdot)\) implies the upper semicontinuity of the multivalued Nemytskij operator generated by \(G\) between two Lebesgue-Bochner spaces. Similar results have been given by the reviewer, \textit{H. T. Nguyen} and \textit{P. P. Zdrejko} in the setting of general ideal spaces [Indag. Math., New Ser. 2, No. 4, 397-409 (1991; Zbl 0748.47051)].
Lebesgue- Bochner spaces, Upper semicontinuity of the multivalued Nemytskij operator; Lebesgue-Bochner spaces, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.), Set-valued operators, upper semicontinuity of the multivalued Nemytskij operator
Lebesgue- Bochner spaces, Upper semicontinuity of the multivalued Nemytskij operator; Lebesgue-Bochner spaces, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.), Set-valued operators, upper semicontinuity of the multivalued Nemytskij operator
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