Linear differential equations of the second order with elementary basic central dispersions. (English) Zbl 0581.34036

This paper investigates differential equations of the type (q) \(y''=q(t)y\), \(q\in C^ 0({\mathbb{R}})\), \(({\mathbb{R}}:=(-\infty,\infty))\) being oscillatory on \({\mathbb{R}}\) (i.e. \(\pm \infty\) are the cluster points of zeros of any (nontrivial) solution of (q)). Equation (q) is often assumed such that its basic central dispersion is elementary. This property occurs e.g. in equation (q) whose coefficient q is a \(\pi\)-periodic function (on \({\mathbb{R}})\). Naturally, not every equation (q) with an elementary basic central dispersion has a \(\pi\)-periodic coefficient. The object of this paper is to investigate conditions under which (q) with an elementary basic central dispersion has a \(\pi\)-periodic coefficient q.


34C99 Qualitative theory for ordinary differential equations
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[1] Borůvka O.: Linear Differential Transformations of the Second Order. The English Universities Press, London, 1971. · Zbl 0218.34005
[2] Борувка О.: Тєоруя глобальных свойсмв обыкновєнных лунєйных дуффєрєнцуалъных уравнєнуй вморого порядка. Дифференциальные уравнения, K28, XII, 1976, 1347-1383.
[3] Borůvka O.: Lectures in the seminar of the Institute of Mathematics of the Czechoslovak Academy of Science in Brno. · Zbl 0218.34005
[4] Borůvka O.: Sur les blocs des équations différentielles y” = q(t)y aux coefficients périodiques. Rend. Mat. (2), 8, S. VI, 1975, 519-532. · Zbl 0326.34007
[5] Borůvka O.: Sur quelques compléments á la théorie de Floquet pour les équations différentielles du deuxième ordre. Ann. mat. p. ed appl., S. IV, CH, 1975, 71-77. · Zbl 0311.34012 · doi:10.1007/BF02410597
[6] Neuman F.: Note on bounded non-periodic solutions of the second-order linear differential equations with periodic coefficients. Mat. Nachrichten, 39, 1969, 217-222. · Zbl 0169.41703 · doi:10.1002/mana.19690390403
[7] Neuman F.: Linear differential equations of the second order and their applications. Rend. Math. (3), Vol. 4, Série VI, 1971, 559-617. · Zbl 0227.34005
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