On N-th order nonlinear ordinary random differential equations - Dhage, B.C. (Нелінійні коливання, 2010)
In this paper, an existence result for a nonlinear n-th order ordinary random differential equation is proved under Caratheodory condition. Two existence results for extremal random solutions are also proved for ´ Caratheodory as well as discontinuous cases of the nonlinearity involved in the equations. Our investigations are placed in the Banach space of continuous real-valued functions on closed and bounded intervals of real line together with the application of random version of Leray – Schauder principle.