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Nonlocal semilinear second-order differential inclusions in abstract spaces without compactness

Martina Pavlačková, Valentina Taddei (2023)

Archivum Mathematicum

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 systems of BVPs with asymptotically superlinear boundary conditions

Christopher S. Goodrich (2012)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider a coupled system of second-order boundary value problems with nonlocal, nonlinear boundary conditions, and we examine conditions under which such problems will have at least one positive solution. By imposing only an asymptotic growth condition on the nonlinear boundary functions, we are able to achieve generalizations over existing works and, in particular, we allow for the nonlocal terms to be able to be realized as Lebesgue-Stieltjes integrals possessing signed Borel...

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