Unique solution of an infinite 2-system model of first order ordinary differential equation

Abstract

This work is to solve an infinite 2-system model of first order ordinary differential equations. The system is in Hilbert space l2 with the coefficients are any positive real numbers. The system is rewritten as a system in the form of matrix equations and it is first studied in ℝ2 where its solution is obtained and a fundamental matrix is constructed. The results are carried out to solve the infinite 2-system in Hilbert space l2 . The control functions satisfy integral constraint and are elements of the space of square integrable function in l2 . The existence and uniqueness of the solution of the system in Hilbert space l2 on an interval time [0, T] for a sufficiently large T is then proven