Asymptotic Instability of Nonlinear Differential Equations
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This article shows that the zero solution to the system
x' = A(t)x + ƒ(t, x), ƒ(t, 0) = 0
is unstable. To show instability, we impose conditions on the nonlinear part ƒ(t, x) and on the fundamental matrix of the linear system y' = A(t)y. Our results generalize the instability results obtained by J. M. Bownds, Hatvani-Pintér, and K. L. Chiou.
CitationAvis, R. & Naulin, R. (1997). Asymptotic instability of nonlinear differential equations. Electronic Journal of Differential Equations, 1997(16), pp. 1-7.
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