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- W2045498701 abstract "let x= (x1, i , x,) and f= (fi, fn), and suppose that f is of class Cl. A set, Q, of points x will be called unrestricted if, whenever a point xo is in Q, the solution path x = x(t), where x0 = x(0), exists for o 0 a 8 = be> 0 such that x(t)-y(t) I 0 a 8=8e>0 such that jx(t)-y(t)j <e whenever y(t) is in Q and Ix(to)-y(to)I <8 holds for some value t=to, oo <to< oo. Of course, in both types of stability, the number 8 depends not only on e but also on the particular solution x(t) considered. The notion of A-stability is that associated with Minding, Dirichlet (in the case of equilibrium solutions), and Liapounoff [5, pp. 98-99; 3, pp. 210-211]. The B-stability was considered by Hartman and Wintner [i]. It is easy to see that a solution which is B-stable is surely A-stable. The converse is false however. In fact, one need only consider the single differential equation (nn 1)" @default.
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- W2045498701 date "1954-03-01" @default.
- W2045498701 modified "2023-09-25" @default.
- W2045498701 title "Stability and almost periodicity in dynamical systems" @default.
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