Nonlinear Volterra delay evolution inclusions subjected to nonlocal initial conditions
DOI:
https://doi.org/10.12775/TMNA.2020.065Słowa kluczowe
Volterra delay evolution inclusion, nonlocal implicit initial condition, $C^0$-solutions, equicontinuous semigroup, global solvabilityAbstrakt
This paper deals with a nonlinear Volterra delay evolution inclusion subjected to a nonlocal implicit initial condition. The evolution inclusion involves an $m$-dissipative operator (possibly multivalued and/or nonlinear) and a noncompact interval. We first consider the evolution inclusion subjected to a local initial condition and prove an existence result for bounded $C^0$-solutions. Then, using a fixed point theorem for upper semicontinuous multifunctions with contractible values, we obtain a global solvability result for the original problem. Finally, we present an example to illustrate the abstract result.Bibliografia
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Prawa autorskie (c) 2021 Topological Methods in Nonlinear Analysis
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