On first and second order linear Stieltjes differential equations
Classical Analysis and ODEs
2021-09-23 v2
Abstract
This work deals with the obtaining of solutions of first and second order Stieltjes differential equations. We define the notions of Stieltjes derivative on the whole domain of the functions involved, provide a notion of n-times continuously Stieltjes-differentiable functions and prove existence and uniqueness results of Stieltjes differential equations in those spaces. We also present the Green's functions associated to the different problems and an application to the Stieltjes harmonic oscillator.
Cite
@article{arxiv.2106.09332,
title = {On first and second order linear Stieltjes differential equations},
author = {Francisco J. Fernández and Ignacio Márquez Albés and F. Adrián F. Tojo},
journal= {arXiv preprint arXiv:2106.09332},
year = {2021}
}
Comments
40 pages, 11 figures