On second-order linear Stieltjes differential equations with non-constant coefficients

0587133 - MÚ 2025 RIV DE eng J - Journal Article
Márquez Albés, Ignacio - Fernández, F. J. - Tojo, F.
On second-order linear Stieltjes differential equations with non-constant coefficients.
Open Mathematics. Roč. 22, č. 1 (2024), č. článku 20240018. ISSN 2391-5455. E-ISSN 2391-5455
Institutional support: RVO:67985840
Keywords : Stieltjes derivative * second-order * uniqueness * Helmholtz equation
OECD category: Pure mathematics
Impact factor: 1.7, year: 2022
Method of publishing: Open access
https://doi.org/10.1515/math-2024-0018

In this work, we define the notions of Wronskian and simplified Wronskian for Stieltjes derivatives and study some of their properties in a similar manner to the context of time scales or the usual derivative. Later, we use these tools to investigate second-order linear differential equations with Stieltjes derivatives to find linearly independent solutions, as well as to derive the variation of parameters method for problems with g-continuous coefficients. This theory is later illustrated with some examples such as the study of the onedimensional linear Helmholtz equation with piecewise-constant coefficients.
Permanent Link: https://hdl.handle.net/11104/0354408