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- W135997404 abstract "This chapter discusses the invariance principle for functional equation. It presents an assumption in which positive limit set ∧+(y) of a solution y(t) of an autonomous differential equation y′ =ƒ(y), whose second member is defined and continuous on some open subset Ω of Rn. A simple and important property is that ∧+(y) ⋂ Ω is an invariant set. There exist quite a number of generalizations of this property to various types of equations, dynamical systems, and processes. of the chapter presents the following three hypotheses: (1) there is only one solution through every initial point; (2) every solution can be continued up to −∞ on the left and +∞ on the right; and (3) the solution y(t) generating the limit set either is bounded or remains in some compact, or closed, subset of Ω. Strauss and Yorke did not need these conditions in their study of asymptotically autonomous differential equations. Certain types of positive pseudoinvariances are easily obtained for unbounded solutions but it is only by adding the requirement that y(t) be uniformly continuous that one is able to ascertain the same types of pseudoinvariances, negative as well as positive." @default.
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- W135997404 date "1976-01-01" @default.
- W135997404 modified "2023-10-16" @default.
- W135997404 title "The Invariance Principle for Functional Equations" @default.
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- W135997404 doi "https://doi.org/10.1016/b978-0-12-164902-9.50031-9" @default.
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