Comparison criteria for the Abel equation of 1st kind
G. A. Grigorian
TL;DR
This paper establishes three comparison criteria for the Abel equation of the first kind, which are used to derive global solvability and closed solution existence criteria, supported by illustrative examples.
Contribution
It introduces new comparison criteria for the Abel equation of the first kind, enhancing understanding of its solvability and solutions.
Findings
Three comparison criteria are proved.
Criteria for global solvability are derived.
Examples demonstrate the results.
Abstract
Three comparison criteria for the Abel equation of 1es kind are proved. The results obtained are used to obtain global solvability criteria and some criteria of existence of closed solutions for the mentioned equation. The results obtained are demonstrated by examples.
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Taxonomy
TopicsNumerical methods for differential equations · Advanced Differential Equations and Dynamical Systems · Nonlinear Differential Equations Analysis