Topological structure of the solution sets to non-autonomous evolution inclusions driven by measures on the half-line. (English) Zbl 07899344
Summary: In this article, we investigate a class of measure differential inclusions of evolution type involving non-autonomous operator with nonlocal condition defined on the half-line. By fixed point theorem, we first obtain some sufficient conditions to ensure the solution set is nonempty, compact, and \(R_\delta\)-set on compact interval. Subsequently, by means of the inverse limit method, we generalize the results on compact interval to noncompact interval. Finally, an example is given to demonstrate the effectiveness of obtained results.
MSC:
| 28B20 | Set-valued set functions and measures; integration of set-valued functions; measurable selections |
| 34G25 | Evolution inclusions |
| 35D30 | Weak solutions to PDEs |
Keywords:
measure evolution inclusions; \(R_\delta\)-set; inverse limit; noncompact interval; nonlocal conditionReferences:
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