This paper presents a theory of differential inequalities for two-point boundary value problems (B.V.Ps) associated with the system of n th order non-linear differential equations. Using these inequalities as a tool we establish the existence and uniqueness of solutions to three-point B.V.Ps associated with the system of n th order non-linear differential equations by using the idea of matching solutions.

This paper presents a criterion for the existence and uniqueness of solutions to two and multipoint boundary value problems associated with annth order nonlinear Lyapunov system. A variation of parameters formula is developed and used as a tool to obtain existence and uniqueness. We discuss solution of the second order problem by the ADI method and develop a fixed point method to find the general solution of thenth order Lyapunov system. The results of Barnett (SIAM J. Appl. Anal.24(1), 1973) are a particular case.

The asymptotic behavior of solutions of Lyapunov type matrix Volterra integro differential equation, in which the coefficient matrices are not stable, is studied by the method of reduction.

Abstract:In this article we derive the solution of higher order Sylster's type differential equation on measure chains in terms of two fundamental matrices. Later by defining the controllability and observability on measure chains, necessary conditions for the controllability and observability of the higher order Sylster's type differential system on measure chains is established.

In this article a typical four point boundary value problem associated with a second order differential equation is proposed. Then its solution is developed with the help of the Green's function associated with the homogeneous equation. Using this idea and Iteration method is proposed to solve the corresponding non linear problem.