On abstract neutral differential equations with state-dependent delay (Q1615288)

This work is about the abstract functional differential equations with state-dependent delay. More precisely, there are established conditions which ensure the existence and the uniqueness of solution for abstract neutral differential equations with state-dependent delay. At the beginning, the concept of solutions for these kind of problem is presented. The main result contains conditions which ensure the existence of a mild solution. The proof is done using the contraction mapping principle. The paper contains an application of the theoretical result and includes new research directions.