Abstract
We establish conditions of asymptotic stability of all solutions of the equation \(\frac{{dx}}{{dt}} = A(x)x\), t≥0in a Banach space E in the case where σ(A(x)⊂{λ:Reλ<0}∀x∈E. We give an example of an equation with unstable solutions.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 2, pp. 264–273, February, 1998.
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Slyusarchuk, V.E. Nonlinear differential equations with asymptotically stable solutions. Ukr Math J 50, 302–313 (1998). https://doi.org/10.1007/BF02513453
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DOI: https://doi.org/10.1007/BF02513453