We study the existence of a mild solution to the nonlocal initial value problem for semilinear second-order differential inclusions in abstract spaces. The result is obtained by combining the Kakutani fixed point theorem with the approximation solvability method and the weak topology. This combination enables getting the result without any requirements for compactness of the right-hand side or of the cosine family generated by the linear operator.
Nonlocal Semilinear second-order inclusions in abstract spaces without compactness / Pavlackovà, Martina; Taddei, Valentina. - In: ARCHIVUM MATHEMATICUM. - ISSN 1212-5059. - 59:1(2023), pp. 99-107. [10.5817/AM2023-1-99]
Nonlocal Semilinear second-order inclusions in abstract spaces without compactness
Valentina Taddei
2023
Abstract
We study the existence of a mild solution to the nonlocal initial value problem for semilinear second-order differential inclusions in abstract spaces. The result is obtained by combining the Kakutani fixed point theorem with the approximation solvability method and the weak topology. This combination enables getting the result without any requirements for compactness of the right-hand side or of the cosine family generated by the linear operator.
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