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Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: In this article, two nonlinear ordinary differential systems, one of which contains impulses are considered, and assuming the existence of bounded solutions, some results on asymptotic equivalence type correspondence between them are obtained.
Abstract: Two nonlinear ordinary differential systems, one of which contains impulses are considered in this note, and assuming the existence of bounded solutions, some results on asymptotic equivalence type correspondence between them are obtained. At the end an open question is posed.
2 citations
2 citations
TL;DR: In this paper, the existence of an asymptotic expansion is characterized by the nice property that a certain quantity F（t) has an approximate linear differential operator in f and admits of a remarkable geometric interpretation as it measures the ordinate of the point wherein that special curve, which has a contact of order n - 1 with the graph of f at the generic point t, intersects a fixed vertical line, say x = T.
Abstract: We call “asymptotic mean” (at +∞) of a real-valued function the number, supposed to exist, , and highlight its role in the geometric theory of asymptotic expansions in the real domain of type (*) where the comparison functions , forming an asymptotic scale at +∞, belong to one of the three classes having a definite “type of variation” at +∞, slow, regular or rapid. For regularly varying comparison functions we can characterize the existence of an asymptotic expansion (*) by the nice property that a certain quantity F（t) has an asymptotic mean at +∞. This quantity is defined via a linear differential operator in f and admits of a remarkable geometric interpretation as it measures the ordinate of the point wherein that special curve , which has a contact of order n - 1 with the graph of f at the generic point t, intersects a fixed vertical line, say x = T. Sufficient or necessary conditions hold true for the other two classes. In this article we give results for two types of expansions already studied in our current development of a general theory of asymptotic expansions in the real domain, namely polynomial and two-term expansions.
2 citations
01 Jan 1995
TL;DR: In this paper, the continuity in norm of the resolvent in the parameter plays the fundamental role in analytic or uniform perturbation theory, and it is shown that under suitable conditions, the possibility of asymptotic expansions of these quantities can be deduced.
Abstract: In the foregoing chapters we have been concerned almost exclusively with analytic or uniform perturbation theory, in which the continuity in norm of the resolvent in the parameter plays the fundamental role. We shall now go into a study in which the basic notion is the strong continuity of the resolvent. Here the assumptions are weakened to such an extent that the analyticity of the resolvent or of the eigenvalues of the operator as functions of the parameter cannot be concluded, but we shall be able to deduce, under suitable conditions, the possibility of asymptotic expansions of these quantities.
2 citations
TL;DR: In this article, asymptotic results in the theory of ordinary differential equations are applied to certain scalar and vector boundary value problems that model various nonlinear dissipative and dispersive wave phenomena.
2 citations