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On the intersection of the set of solutions of two Kummer’s differential equations. (English) Zbl 0596.34014

Let \(y''=p(t)y\) and \(y''=q(t)y\) be oscillatory differential equations. The author investigates the structure of sets of common solutions (resp. increasing solutions, decreasing solutions) of two Kummer differential equations: \((*)\quad -\{X,t\}+X'{}^ 2 p(X)=q(t)\) and \((**)\quad - \{X,t\}+X'{}^ 2 P(X)=Q(t)\) where \(\{X,t\}=(1/2)(X'''(t)/X'(t))- (3/4)(X''(t)/X'(t))^ 2\) is the Schwarz derivative and P,Q\(\in C({\mathbb{R}})\), \(P-Q\in C^ 2({\mathbb{R}})\).
Reviewer: D.Bobrowski

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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References:

[1] Borůvka O.: Linear Differential Transformations of the Second Order. The English Univ. Press, London 1971. · Zbl 0218.34005
[2] Борувка О.: Теория глобальных свойств обыкновенных линейных дифференциальных уравнений второго порядка. Дифференциальные уравнения, No 8, t. 12, 1976, 1347-1383. · Zbl 1170.01332
[3] Borůvka O.: Lectures at the seminar of the Institute of Mathematics of the Czechoslovak Academy of Science in Brno. · Zbl 0218.34005
[4] Staněk S.: On a structure of the intersection of the set of dispersions of two second-order linear differential equations. Acta Univ. Palackianae Olomucensis, F. R. N., T. 73, 1982, 79-85. · Zbl 0543.34026
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