Periodicity of solutions for non-autonomous neutral functional differential equations with state-dependent delay (Q6103317)

The aim of this work is to prove the existence of a periodic solution for some non-autonomous neutral partial functional differential equations with state dependent delay. The phase space is axiomatically defined. The linear part is assumed to generate an evolution family. The nonlinear part is assumed to be continuous and Lipschitzian with respect to the second argument. The authors assume that the family generated by the linear part is exponentially stable. Firstly, the authors prove the existence and uniqueness of a mild solution by using Banach's fixed point theorem. Sufficient conditions are given to prove the existence of a periodic solution and its stability.