## 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
Full Text:

### 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.