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On singularly perturbed ordinary differential equations with measure-valued limits

Zvi Artstein (2002)

Mathematica Bohemica

The limit behaviour of solutions of a singularly perturbed system is examined in the case where the fast flow need not converge to a stationary point. The topological convergence as well as information about the distribution of the values of the solutions can be determined in the case that the support of the limit invariant measure of the fast flow is an asymptotically stable attractor.

On some properties of the solution of the differential equation u ' ' + 2 u ' r = u - u 3

Valter Šeda, Ján Pekár (1990)

Aplikace matematiky

In the paper it is shown that each solution u ( r , α ) ot the initial value problem (2), (3) has a finite limit for r , and an asymptotic formula for the nontrivial solution u ( r , α ) tending to 0 is given. Further, the existence of such a solutions is established by examining the number of zeros of two different solutions u ( r , α ¯ ) , u ( r , α ^ ) .

On strongly asymptotically developable functions and the Borel-Ritt theorem

J. Sanz, F. Galindo (1999)

Studia Mathematica

We show that the holomorphic functions on polysectors whose derivatives remain bounded on proper subpolysectors are precisely those strongly asymptotically developable in the sense of Majima. This fact allows us to solve two Borel-Ritt type interpolation problems from a functional-analytic viewpoint.

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