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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Asymptotic stability for abstract nonlinear functional differential equations

Author: G. F. Webb
Journal: Proc. Amer. Math. Soc. 54 (1976), 225-230
MSC: Primary 34K20; Secondary 47H15
MathSciNet review: 0402237
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Abstract: The nonlinear autonomous functional differential equation $ \dot x(t) = f(x(t)) + g({x_t}),t \geqslant 0,{x_0} = \phi $ is investigated by means of the theory of semigroups of nonlinear operators. The properties of the semigroup associated with this equation provide stability information about the solutions.

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Keywords: Autonomous functional differential equation, stability, asymptotic stability, nonlinear accretive operator, nonlinear semigroup of operators
Article copyright: © Copyright 1976 American Mathematical Society