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- W2034697838 abstract "The purpose of this paper is to extend a well-known theorem of Lyapunov on matrices to unbounded linear operators in an infinite-dimensional Banach space by using semigroup theory. This extension is used for the study of stability problems of nonlinear differential equations. In the special case of a Hilbert space, a direct extension of Lyapunov’s theorem for a bounded operator is obtained; and in the general case of a Banach space the idea of equivalent semi-inner products is introduced. Applications are given to a class of initial boundary value problems in a bounded domain in $R^n $ under nonlinear perturbations." @default.
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- W2034697838 date "1972-05-01" @default.
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- W2034697838 title "Semigroups and Asymptotic Stability of Nonlinear Differential Equations" @default.
- W2034697838 doi "https://doi.org/10.1137/0503035" @default.
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