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On oscillation of solutions of forced nonlinear neutral differential equations of higher order

N. Parhi, Radhanath N. Rath (2003)

Czechoslovak Mathematical Journal

In this paper, necessary and sufficient conditions are obtained for every bounded solution of [ y ( t ) - p ( t ) y ( t - τ ) ] ( n ) + Q ( t ) G y ( t - σ ) = f ( t ) , t 0 , ( * ) to oscillate or tend to zero as t for different ranges of p ( t ) . It is shown, under some stronger conditions, that every solution of ( * ) oscillates or tends to zero as t . Our results hold for linear, a class of superlinear and other nonlinear equations and answer a conjecture by Ladas and Sficas, Austral. Math. Soc. Ser. B 27 (1986), 502–511, and generalize some known results.

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