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On a fundamental central dispersion of the first kind and the Abel functional equation in strongly regular spaces of continuous functions. (English) Zbl 0714.34112

The paper deals with the distribution of zeros of continuous functions which oscillate on the whole real axis. The distribution of zeros of a special class of such functions is expressed by the Abel functional equation. The results are applied to linear differential equations of second order with oscillating solutions.
Reviewer: T.Dłotko

MSC:

34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
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] Borůvka O.: Linear Differential Transformations of the Second Order. The English University Press, London 1971. · Zbl 0218.34005
[2] Laitochová J.: On a Canonical Two-dimensional Space of Continuous Functions. ACTA UPO Vol.91, 1988, in print. · Zbl 0692.46019
[3] Laitochová J.: On Two-dimensional Linear Spaces of Continuous Functions of the Same Character. ACTA UPO Vol.94, 1989, in print. · Zbl 0704.34044
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