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Asymptotic instability of nonlinear differential equations. (English) Zbl 0888.34045
Summary: This article shows that the zero solution to the system \[ x'=A(t)x+f(t,x),\quad f(t,0)=0 \] is unstable. To show instability, we impose conditions on the nonlinear part \(f(t,x)\) and on the fundamental matrix of the linear system \(y'=A(t)y\). Our results generalize the instability results obtained by J. M. Bownds, Hatvani-Pintér, and K. L. Chiou.
MSC:
34D20 Stability of solutions to ordinary differential equations
39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations
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