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A role of Abel’s equation in the stability theory of differential equations. (English) Zbl 0215.43803

MSC:
34D99 Stability theory for ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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References:
[1] Bellman, R.,Stability Theory of Differential Equations (McGraw-Hill, New York – Toronto – London 1953). · Zbl 0053.24705
[2] Boruvka, O.,Lineare Differential transformationen 2. Ordnung (VEB Deutscher Verlag der Wiss., Berlin 1967 [Hochschulbücher für Math., Band 67]).
[3] Cesari, L.,Asymptotic Behavior and Stability Problems in Ordinary Differential Equations (2nd ed., Academic Press, New York, N.Y., Springer Verlag, Berlin – Göttingen – Heidelberg 1963 [Ergebnisse der Mathematik und ihrer Grenzgebiete (N.F.), Band 16]). · Zbl 0111.08701
[4] Hille, E.,Lectures on Ordinary Differential Equations (Addison-Wesley, Reading, Mass. – London – Don Mills, Ont. 1969). · Zbl 0179.40301
[5] Kuczma, M.,Functional Equations in a Single Variable (Polska Akad. Nauk, Warszawa 1968 [Monografie Matematyczne, Vol. 46]). · Zbl 0196.16403
[6] Kuczma, M.,A Survey of the Theory of Functional Equations (Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz., No. 130, Beograd 1964). · Zbl 0154.16601
[7] Neuman, F.,Relations Between the Distribution of the Zeros of the Solutions of a 2 nd-Order Linear Differential Equation and the Boundedness of These Solutions, Acta Math. Acad. Sci. Hungar.19, 1–6 (1968). · Zbl 0162.12304
[8] Neuman, F.,Centroaffine Invariants of Plane Curves in Connection with the Theory of the Second-Order Linear Differential Equations, Arch. Math. (Brno)5, 201–216 (1968). · Zbl 0218.34007
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