PERIODIC BOUNDARY VALUE PROBLEMS OF SECOND ORDER RANDOM DIFFERENTIAL EQUATIONS

In this paper, an existence and the existence of extremal random solutions are proved for a periodic boundary value problem of second order ordinary random differential equations. Our investigations have been placed in the space of real-valued functions defined and continuous on closed and bounded intervals of real line together with the applications of the random version of a nonlinear alternative of Leray-Schauder type and an algebraic random fixed point theorem of Dhage [5]. An example is also indicated for demonstrating the realizations of the abstract theory developed in this paper.