Note on the stability for linear systems of differential equations
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Abstract
In this paper, by applying the fixed point alternative method, we give a necessary and sufficient condition in order that the first order linear system of differential equations $ \dot z(t) + A(t)z(t) + B(t) = 0 $ has the Hyers-Ulam-Rassias stability and find Hyers-Ulam stability constant under those conditions. In addition to that we apply this result to a second order differential equation $ \ddot y(t) + f(t)\dot y(t) + g(t)y(t) + h(t) = 0 $.
Keywords: Fixed point method; Hyers-Ulam-Rassias stability; System of dierential equations.
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