Asymptotic Instability of Nonlinear Differential Equations
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This article shows that the zero solution to the system xi = A(t)x + f(t, x), f(t, 0) = 0 is unstable. To show instability, we impose conditions on the nonlinear part f(t, x) and on the fundamental matrix of the linear system yi = A(t)y. Our results generalize the instability results obtained by J. M. Bownds, Hatvani-Pint´er, and K. L. Chiou.