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The asymptotical solving of the equation \(y'=A(t)y\), with a 2\(\times 2\) matrix A in the oscillation case. II. (Italian. English summary) Zbl 0643.34066

A previous paper [Part I, ibid. 74, 175-203 (1985; Zbl 0579.34024)] on asymptotical solutions of oscillatory systems of two first order linear differential equations is continued; asymptotic value of the extrema of solutions are given, with strict numerical bounds.

MSC:

34E05 Asymptotic expansions of solutions to ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

Citations:

Zbl 0579.34024
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References:

[1] M. Bartusek , Properties of oscillating solutions of two-dimensional differential systems , Proceedings of the I. N. Vekna Institute of Applied Mathematics, 8 , pp. 5 - 12 . MR 650581 · Zbl 0483.34030
[2] A.M. Bresquar , Sulla risoluzione asintotica dell’equazione y’ = A(t)y, con A(t) matrice 2 \times 2, nel caso oscillante , in corso di stampa su Rend. Sem. Mat. Univ. Padova , 74 ( 1985 ). Numdam | Zbl 0579.34024 · Zbl 0579.34024
[3] L. Cesari , Asymptotic behavior and stability problems in ordinary differential equations , Springer , Berlin , 1963 . Zbl 0111.08701 · Zbl 0111.08701
[4] W. Hahn , Theory and Application of Liapunov’s Direct Method , Prentice-Hall , 1963 . MR 147716 | Zbl 0119.07403 · Zbl 0119.07403
[5] E. Heil , Oscillatory and nonoscillatory systems of two first order linear differential equations , Colloq. Math. Soc. Janos Bolyai , 30 , North-Holland , 1981 . MR 680605 | Zbl 0426.34023 · Zbl 0426.34023
[6] W.T. Reid , Sturmian Theory for Ordinary Differential Equations , Springer , New York , 1980 . MR 606199 | Zbl 0459.34001 · Zbl 0459.34001
[7] U. Richard , Sulla risoluzione asintotico-numerica dell’equazione differenziale (py’)’ + qy = 0 nel caso oscillante , Atti Accad. Sci. Torino , 97 ( 1962 -63), pp. 857 - 890 . MR 155046 | Zbl 0237.65052 · Zbl 0237.65052
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