Basic theory of a class of linear functional differential equations with multiplication delay
Classical Analysis and ODEs
2018-01-29 v4 Mathematical Physics
Analysis of PDEs
Functional Analysis
math.MP
Abstract
By introducing a kind of special functions namely exponent-like function, cosine-like function and sine-like function, we obtain explicitly the basic structures of solutions of initial value problem at the original point for this kind of linear pantograph equations. In particular, we get the complete results on the existence, uniqueness and non-uniqueness of the initial value problems at a general point for the kind of linear pantograph equations.
Cite
@article{arxiv.1605.06734,
title = {Basic theory of a class of linear functional differential equations with multiplication delay},
author = {Cheng-shi Liu},
journal= {arXiv preprint arXiv:1605.06734},
year = {2018}
}
Comments
44 pages, no figure. This is a revised version of the third version of the paper. Some new results and proofs have been added