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Linear differential Lappo-Danilevskii systems

S. A. Mazanik (2002)

Mathematica Bohemica

The class of linear differential systems with coefficient matrices which are commutative with their integrals is considered. The results on asymptotic equivalence of these systems and their distribution among linear systems are given.

Linearisation of second-order differential equations.

Eduardo Martínez (1996)

Extracta Mathematicae

Given a second order differential equation on a manifold we find necessary and sufficient conditions for the existence of a coordinate system in which the system is linear. The main tool to be used is a linear connection defined by the system of differential equations.

Linearization technique for oscillation of perturbed half-linear differential equations

Manabu Naito (2025)

Archivum Mathematicum

It is shown that oscillation of perturbed second order half-linear differential equations can be derived from oscillation of second order linear differential equations associated with modified Riccati equations. In the main result of the present paper, some of technical assumptions in the known results of this type are removed.

Linearized comparison criteria for a nonlinear neutral differential equation

Xinping Guan, Sui Sun Cheng (1996)

Annales Polonici Mathematici

A class of nonlinear neutral differential equations with variable coefficients and delays is considered. Conditions for the existence of eventually positive solutions are obtained which extend some of the criteria existing in the literature. In particular, a linearized comparison theorem is obtained which establishes a connection between our nonlinear equations and a class of linear neutral equations with constant coefficients.

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