Existence of solutions and periodic solutions of a neutral measure functional differential equation with infinite delay

This paper focuses on the study of existence of solutions and periodic solutions for a general class of neutral measure functional differential equations (NMFDEs for short) with infinite delay. The relationship between solutions of NMFDEs with infinite delay and solutions of generalized ordinary differential equations is first discussed, based on this the existence, uniqueness and continuous dependence of solutions for NMFDEs with infinite delay are investigated. Then the existence of periodic solutions for the considered equation is also studied and the corresponding sufficient conditions are obtained by fixed-point principle. Finally two examples are given to illustrate the main obtained results. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.