Laitochová, Jitka 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 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 28, 165-175 (1989). 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 Cited in 3 Documents 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 Keywords:distribution of zeros; Abel functional equation; linear differential equations of second order with oscillating solutions PDFBibTeX XMLCite \textit{J. Laitochová}, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 28, 165--175 (1989; Zbl 0714.34112) Full Text: EuDML 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 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.