On first and second order linear Stieltjes differential equations
Francisco J. Fernández, Ignacio Márquez Albés, F. Adrián F. Tojo
Abstract
This work deals with the obtaining of solutions of first and second order Stieltjes differential equations. We define the notion 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 the space of such functions. We also present the Green's functions associated to the different problems and an application to the Stieltjes harmonic oscillator.
Topics & Concepts
Riemann–Stieltjes integralMathematicsUniquenessMathematical analysisDifferential equationDifferentiable functionOrder (exchange)Space (punctuation)Pure mathematicsIntegral equationLinguisticsEconomicsFinancePhilosophyNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsAdvanced Mathematical Modeling in Engineering