Address:
Department of Applied Mathematics, Moravian Business College Olomouc, tř. Kosmonautů 1288/1, 779 00 Olomouc, Czech Republic
Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, Via G. Amendola, 2 - pad. Morselli, I-42122 Reggio Emilia, Italy
E-mail:
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.
AMSclassification: primary 34A60; secondary 34G25.
Keywords: second-order differential inclusion, nonlocal conditions, Banach spaces, cosine family, approximation solvability method, mild solution.
DOI: 10.5817/AM2023-1-99