Semiflows for differential equations with locally bounded delay on solution manifolds in the space \(C^1 ((-\infty, 0], {\mathbb R}^n)\)
In this big, interesting paper, with interesting results and nicely prepared, the author presents a construction of semiflow for autonomous differential equations with unbounded (locally bounded) delay. Some special cases of the problem, have been considered by the author in several other papers. Basic information about that are contained in the introduction. Also many ideas used in the paper (tangent cone, special Fréchet spaces, special Banach spaces, and some results used in the sequel) are presented with proofs in preliminaries. Special part of the paper is devoted for the properties of the ``semiflow on the solution manifold''. As it is stated by the author, the result presented in the paper, applies to autonomous differential equations with state-dependent delay which may be unbounded but which is locally bounded. ``The case of constant bounded delay, distributed or not, is included''. In my opinion, this paper requires from readers wide knowledge of mathematical ideas.
semiflow for differentialequation with delay
scientific article; zbMATH DE number 6712731