Geodesic
Nonlocal semilinear second-order differential inclusions in abstract spaces without compactness
Archivum mathematicum, Tome 59 (2023) no. 1, pp. 99-107

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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.
DOI : 10.5817/AM2023-1-99
Classification : 34A60, 34G25
Keywords: second-order differential inclusion; nonlocal conditions; Banach spaces; cosine family; approximation solvability method; mild solution 
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Pavlačková, Martina; Taddei, Valentina. Nonlocal semilinear second-order differential inclusions in abstract spaces without compactness. Archivum mathematicum, Tome 59 (2023) no. 1, pp. 99-107. doi: 10.5817/AM2023-1-99

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