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Keywords:
second-order differential inclusion; nonlocal conditions; Banach spaces; cosine family; approximation solvability method; mild solution
second-order differential inclusion; nonlocal conditions; Banach spaces; cosine family; approximation solvability method; mild solution
Summary:
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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