EXISTENCE RESULT FOR PERIODIC BOUNDARY VALUE PROBLEM OF SET DIFFERENTIAL EQUATIONS USING MONOTONE ITERATIVE TECHNIQUE

The study of set differential equations(SDE)[1] is useful as it encompasses the study of scalar differential equations and vector differential equations as special cases and further this study is done in a semilinear metric space. The monotone iterative technique (MIT) [2] is a flexible mechanism to obtain monotone sequence that converge to the extremal solutions of the considered problem. The study of periodic boundary value problems(PBVP) is complicated and more so in the case of SDEs, where the constraints are many. Hence the construction of MIT for PBVP for set differential equations has not been done till now. In [3] MIT for PBVP was developed using monotone sequences, which are solutions of the initial value problem [IVPs] of linear differential equations. These solutions are unique and hence the monotone sequences obtained are unique and they converge to a unique function which is shown to be a solution of the considered PBVP. The special advantage obtained with this approach is that working with IVPs of linear differential equations is easy and the uniqueness of the solution of the PBVP is guaranteed with no extra assumptions or effort. In this paper, using the approach utilized in [3] we develop the MIT for PBVP for SDEs.