Unique solution of an infinite 2-system model of first order ordinary differential equation
Date
2023-04Author
Muhammad Arif Syazani, Mohd Yazid
Gafurjan Ibragimov
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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