Abstract
This article is mainly devoted to the study of the existence of solutions for second-order abstract non-autonomous integro-differential evolution equations with infinite state-dependent delay. In the first part, we are concerned with second-order abstract non-autonomous integro-differential retarded functional differential equations with infinite state-dependent delay. In the second part, we extend our results to study the second-order abstract neutral integro-differential evolution equations with state-dependent delay. Our results are established using properties of the resolvent operator corresponding to the second-order abstract non-autonomous integro-differential equation and fixed point theorems. Finally, an application is presented to illustrate the theory obtained.
Highlights
Differential systems that exhibit state-dependent delay frequently emerge when modeling physical phenomena
Motivated by the theory developed in the works mentioned previously, our objective in this article is to study the existence of mild solutions for non-autonomous second-order abstract integro-differential evolution equations with infinite state-dependent delay of the following form: z 00 (t) = A(t)z(t) +
The main focus of this paper is on finding mild solutions for second-order abstract non-autonomous integro-differential evolution systems with infinite state-dependent delay
Summary
Henríquez 3,† , Velusamy Vijayakumar 4,† , Kottakkaran Sooppy Nisar 5, *,†.
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