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On solutions of the vector functional equation \(y(\xi(X))=f(X)\cdot A\cdot y(X)\). (English) Zbl 0375.34013


MSC:

34A30 Linear ordinary differential equations and systems
39B42 Matrix and operator functional equations
39B05 General theory of functional equations and inequalities
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34C25 Periodic solutions to ordinary differential equations
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References:

[1] Boruvka, O.,Linear differential transformations of the second order. The English Universities Press, London, 1971. · Zbl 0222.34002
[2] Kuczma, M.,Functional equations in a single variable, PWN, Warszawa, 1968. · Zbl 0196.16403
[3] Neuman, F.,Linear differential equations of the second order and their applications. Rend. Mat.4 (1971), 559–617. · Zbl 0227.34005
[4] Neuman, F.,A role of Abel’s equation in the stability theory of differential equations. Aequationes Math.6 (1971), 66–70. · Zbl 0215.43803
[5] Neuman, F.,L 2-solutions of y” = q(t)y and a functional equation. Aequationes Math.6 (1971), 162–169. · Zbl 0225.34022
[6] Neuman, F.,Distribution of zeros of solutions of y” = q(t)y in relation to their behaviour in large. Studia Sci. Math. Hungar.8 (1973), 177–185. · Zbl 0286.34050
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[8] Stäckel, P.,Über Transformationen von Differentialgleichungen. J. Reine Angew. Math.111 (1893), 290–302. · JFM 25.0167.01
[9] Wilczynski, E. J.,Projective differential geometry of curves and ruled surfaces. B. G. Teubner, Leipzig, 1906. · JFM 37.0620.02
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