Diferenciālvienādojumu asimptotiskā ekvivalence
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Latvijas Universitāte
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Abstract
Bakalaura darbā atrasti nepieciešamie nosacījumi divu parasto diferenciālvienādojumu asimptotiskai ekvivalencei. Apskatīti gadījumi, kad diferenciālvienādojumu lineārā daļa ir ar konstantiem koeficientiem (Levinsona teorēma), kā arī vispārinājums diferenciālvienādojumam, kur lineārā daļa ir ar mainīgiem koeficientiem, izmantojot atšķirīgu pierādījumu metodi.
Atslēgas vārdi: asimptotiskā ekvivalence, homeomorfisms, Košī matrica.
In this thesis we establish the necessary conditions for the asymptotic equivalence of two ordinary differential equations. We consider two cases: 1. When the linear part of the differential equation has constant coefficients (Levinson’s theorem) and 2. A more general case with time-dependent coefficients of the linear part. A novel proof technique is presented. Keywords: asymptotic equivalence, homeomorphism, Cauchy matrix.
In this thesis we establish the necessary conditions for the asymptotic equivalence of two ordinary differential equations. We consider two cases: 1. When the linear part of the differential equation has constant coefficients (Levinson’s theorem) and 2. A more general case with time-dependent coefficients of the linear part. A novel proof technique is presented. Keywords: asymptotic equivalence, homeomorphism, Cauchy matrix.