Stability of abstract nonlinear nonautonomous differential-delay equations with unbounded history-responsive operators |
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Authors: | MI Gil' |
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Institution: | Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel |
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Abstract: | We consider a class of nonautonomous functional-differential equations in a Banach space with unbounded nonlinear history-responsive operators, which have the local Lipshitz property. Conditions for the boundedness of solutions, Lyapunov stability, absolute stability and input-output one are established. Our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators. |
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Keywords: | Abstract nonlinear differential-delay equations Lyapunov stability Absolute stability Input-output stability Boundedness of solutions |
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