Generalized chain rules and applications to Stieltjes differential and integral equations

DOI10.1007/s00025-023-02104-0OpenAlexW4391143586WikidataQ129417015 ScholiaQ129417015MaRDI QIDQ6185797

Ignacio Márquez Albés, Antonín Slavík

Publication date: 30 January 2024

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-023-02104-0

zbMATH Keywords

exponential functionStieltjes integralchain ruleproduct rulepower ruleBernoulli differential equationStieltjes derivative

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Integrals of Riemann, Stieltjes and Lebesgue type (26A42) Explicit solutions, first integrals of ordinary differential equations (34A05) Generalized ordinary differential equations (measure-differential equations, set-valued differential equations, etc.) (34A06)

Cites Work

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• Theory and applications of first-order systems of Stieltjes differential equations
• Generalized elementary functions
• Chain rule and invariance principle on measure chains
• A new unification of continuous, discrete and impulsive calculus through Stieltjes derivatives
• Duality for Stieltjes differential and integral equations
• Miscellaneous dynamic equations
• On first and second order linear Stieltjes differential equations
• Chain rules and p-variation
• Regulated functions and the Perron-Stieltjes integral
• Kurzweil–Stieltjes Integral
• Notes on the linear equation with Stieltjes derivatives
• The logistic equation in the context of Stieltjes differential and integral equations

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