## Limit behavior of solutions of ordinary linear differential equations.(English)Zbl 0809.34019

The author deals with the set of all linear differential equations $y^{(n)}+ p_{n-1}(x) y^{(n-1)}+\cdots+ p_ 0(x) y=0$ with continuous coefficients on open intervals. The global transformability decomposes the set into classes of equivalent equations.
The goal of the paper is the characterization of each class by means of the $$\omega$$-limit set taken for any $$n$$-tuple of linearly independent solutions.
Reviewer: E.Barvínek (Brno)

### MSC:

 34A30 Linear ordinary differential equations and systems 34D05 Asymptotic properties of solutions to ordinary differential equations 34A26 Geometric methods in ordinary differential equations 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations
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### References:

 [1] N.V. Azbelev and Z.B. Caljuk, On the question of distribution of zeros of solutions of third order linear differential equation. (Russian)Mat. Sb. (N.S.) 51 (1960), 475–486. [2] J.H. Barrett, Oscillation theory of ordinary differential equations.Adv. in Math. 3 (1969), 451–509. · Zbl 0213.10801 [3] G.D. Birkhoff, On the solutions of ordinary linear homogeneous differential equations of the third order.Ann. of Math. 12 (1910/11), 103–127. · JFM 42.0344.01 [4] O. Boruvka, Linear differential transformations of the second order.The English Univ. Press, London, 1971. · Zbl 0222.34002 [5] W.A. Coppel, Disconjugacy. Lecture Notes in Math.220,Springer,Berlin, 1971. [6] M. Greguš, Linear differential equations of the third order.North Holland, Reidel Co, Dordrecht-Boston-Lancaster, 1986. [7] G.B. Gustafson, Higher order separation and comparison theorems, with applications to solution space problems.Ann. Mat. Pura Appl. (4)95 (1973), 245–254. · Zbl 0282.34026 [8] M. Hanan, Oscillation criteria for third order linear differential equations.Pacific J. Math. 11 (1961), 919–944. · Zbl 0104.30901 [9] I.T. Kiguradze and T.A. Chanturija, Asymptotic properties of solutions of nonautonomous ordinary differential equations. (Russian) ”Nauka,”Moscow, 1990. [10] V.V. Nemytskii and V.V. Stepanov, Qualitative theory of differential equations. (Russian) ”Gostekhizdat,”Moscow-Leningrad, 1949. · Zbl 0089.29502 [11] F. Neuman, Geometrical approach to linear differential equations of then-th order.Rend. Mat. 5 (1972), 579–602. · Zbl 0257.34029 [12] F. Neuman, On two problems about oscillation of linear differential equations of the third order.J. Diff. Equations 15 (1974), 589–596. · Zbl 0287.34029 [13] F. Neuman, Global properties of linear differential equations. (Mathematics and Its Applications, East European Series52)Kluwer Acad. Publ. & Academia, Dordrecht-Boston-London & Praha, 1991. · Zbl 0784.34009 [14] G. Sansone, Equazioni differenziali nel campo reale,Zanichelli, Bologna, 1948. · Zbl 0041.41903 [15] C.A. Swanson, Comparison and oscillation theory of linear differential equations. Academic Press,New York-London, 1968. · Zbl 0191.09904
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