Existence and uniqueness of solution for Stieltjes differential equations with several derivators
The paper deals with systems of nonlinear first-order Stieltjes differential equations of the form \[ (x_i)'_{g_i}(t)=f_i(t,x(t)),\quad i\in\{1,\ldots,n\}, \] in which each component \(x_i\) is being differentiated with respect to a different derivator \(g_i\) (a nondecreasing and left-continuous function). The authors consider initial-value problems for this type of systems, and establish analogues of the Osgood uniqueness theorem, Montel-Tonelli uniqueness theorem, as well as sufficient conditions for the existence of solutions.
scientific article; zbMATH DE number 7388021
scientific article