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Oscillatory properties of solutions of second order nonlinear neutral differential inequalities with oscillating coefficients

Myron K. Grammatikopoulos;  Pavol Marušiak — 1995

Archivum Mathematicum

This paper deals with the second order nonlinear neutral differential inequalities ( A ν ) : ( - 1 ) ν x ( t ) { z ' ' ( t ) + ( - 1 ) ν q ( t ) f ( x ( h ( t ) ) ) } ≤ 0 , t ≥ t 0 ≥ 0 , where ν = 0 or ν = 1 , z ( t ) = x ( t ) + p ( t ) x ( t - τ ) , 0 < τ = const, p , q , h : [ t 0 , ∞ ) → R f : R → R are continuous functions. There are proved sufficient conditions under which every bounded solution of ( A ν ) is either oscillatory or lim inf t → ∞ | x ( t ) | = 0 .

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