Stability and boundedness of solutions of Stieltjes differential equations (Q1412975)

The authors develop basic qualitative theory for Stieltjes differential equations, which essentially are Stieltjes integral equations based on a so called time integrator function \(m(t)\). Whereas \(m(t) =t\) reduces to the case of an ordinary differential equation, other time integrators are connected to ordinary difference equations or many other types of equations on so called time scales. Within this framework the paper contains considerations about existence, representations and estimates of generalized exponential functions. The main theorems are concerned with boundedness, stability and continuous dependence on the time integrator of solutions of quasi-linear Stieltjes differential equations.