Existence and uniqueness of \(C^{1+\alpha}\)-strict solutions for integro-differential equations with state-dependent delay. (Q2423437)

In the paper, the problem of the existence of a solution to the initial value problem for an abstract integro-differential equations with a state-dependent delay is studied. The main result of the paper (namely, Theorem 3) deals with the local existence of the so-called \(C^{1+\alpha}\)-strict solution. The results obtained are applied and further discussed in Section 4, where some examples concerning partial differential equations are presented.