On the Oscillation of Solutions of a Higher Order Nonlinear Neutral Functional Differential Equation with an Oscillating Coefficient

Abstract

In this paper, we are concerned with the oscillation of the solutions of a certain more general higher order nonlinear neutral type functional differential equation with an oscillating coefficient of the form where n> 2; P. (/),Qj (/),r,. (¿) e C[tQ,+co) for i = 1,2,- • •,zw ; T* (/) is an oscillatory function for z = l,2,***,m ; Qi (7) is positive valued for i = l,2,---,m. <Ji (/) G C [/0,+oo) ? 0, a i (/)</; cr. (i)—»+ oo as t —» oo for / = l,2,***,m; ri (/)->+oo as / —> oo for z = 1,2,* • •,m is a nondecreasing function, uji (i/) > 0 for u ^ 0 and i = 1,2?* • •, m . We obtained two sufficient criteria for oscillatory behaviour of its solutions. Mathematics Subject Classification: 34K11Bu çalışmada; n> 2 , i = 1,2, • - • ? m için ^(/),ö.(i),rf.(i)eC[/0,+oo); z = 1,2, —için P.(t) 1er salmımlı fonksiyonlar; z = 1,2, —,w için Qı (/) 1er pozitif değerli fonksiyonlar; <7j (/) e Cf[/0,+oo) , er' (/) > 0, crj (7) < t ve t —> oo iken z = l,2, — , m için tj —> +oo ; z = 1,2, —,m için f^lı^EC(i?, 7?) ler azalmayan fonksiyonlar ve u ^ 0 iken uf^u) > 0 olmak üzere m v > m y (d+2A (d W (0) + Zö/ (d/ (y (v (d))=0 /=1 J /=1 tipindeki yüksek mertebeden lineer olmayan diferensiyel denklemin çözümlerinin salmımlılığı üzerine yeter şartlı iki kriter elde edilmektedir.