Oscillations in Higher-Order Neutral Differential Equations

Philos, CH. G. ; Purnaras, I. K. ; Sficas, Y. G.

Canadian journal of mathematics, Tome 45 (1993) no. 1, pp. 132-158

Résumé

Consider the n-th order (n ≥ 1 ) neutral differential equation where σ1 < σ 2 < ∞ and μ and η are increasing real-valued functions on [Ƭ 1, Ƭ 2] and [σ1, σ2] respectively. The function μ is assumed to be not constant on [Ƭ 1, Ƭ 2] and [Ƭ 1, Ƭ 2] for every Ƭ ∈ (Ƭ 1, Ƭ 2) similarly, for each σ ∈ (σ1, σ2), it is supposed that r\ is not constant on [σ1 , σ] and [σ, σ2]. Under some mild restrictions on Ƭ 1,- and σ1, (ι = 1,2), it is proved that all solutions of (E) are oscillatory if and only if the characteristic equation of (E) has no real roots.

Détail

DOI : 10.4153/CJM-1993-008-6

Mots-clés : 34K15, oscillation, neutral differential equation

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