On the existence of periodic and bounded solutions for functional differential equations of pointwise type with a strongly nonlinear right-hand side
There is a one-to-one corresponcence between the traveling-wave-type solutions of infinite-dimensional dynamical systems and the solutions of functional-differential equations of pointwise type. The approach proposed for the study of such equations is based on a formalism whose central element is the construction of a finitely generated group \(Q\) of homeomorphisms of the line (the group operation in such a group is the superposition of two homeomorphisms). The type of functional-differential equations considered here is rather wide. At the same time, the use of the specifics of such a class of equations related to group features makes it possible to obtain advanced results for them and also to establish obstacles that prevent such equations from inheriting remarkable properties of solutions of ordinary differential equations. The main idea is from the work of \textit{L. A. Beklaryan} [Izv. Math. 84, No. 2, 209--245 (2020; Zbl 1458.34120); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 84, No. 2, 3--42 (2020)].
scientific article; zbMATH DE number 7291204