Existence and Stability of Solutions for Linear and Nonlinear Stieltjes Differential Equations(1)

This paper deals with Cauchy problems and nonlocal problems for non-linear Stieltjes differential equations corresponding to a certain function g. We establish existence and uniqueness results for nonlinear equations with initial value or nonlocal conditions in the space x212c; x1d49e;(g) ([0, H], Double-struck capital R) using fixed point methods and g-topology theory. We introduce the concepts of Ulam-Hyers (UH) and generalized Ulam-Hyers-Rassias (UHR) stability and present Ulam type stability results for linear and nonlinear equations in the spaces x1d49c; x1d49e;(g) ([0, H], Double-struck capital R) subset of x212c; x1d49e;(g) ([0, H], Double-struck capital R) and x212c; x1d49e;(g) ([0, H], Double-struck capital R). Finally, numerical examples are given to illustrate our results.