In this paper, the authors investigated oscillatory and asymptotic behavior of solutions of a class of nonlinear higher order neutral differential equations with positive and negative coefficients. The results in this paper generalize the results of Tripathy, Panigrahi and Basu [5]. We establish new conditions which guarantees that every solution either oscillatory or converges to zero. Moreover, using the Banach Fixed Point Theorem sufficient conditions are obtained for the existence of bounded positive solutions. Examples are considered to illustrate the main results.
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In this paper, Oscillatory and asymptotic behaviour of solutions of a class of nonlinear fourth order neutral differential equations with positive and negative coefficients of the form (H) (r(t)(y(t) + p(t)y(t - τ))")" + q(t)G(y(t - α)) - h(t) H (y(t - β)) = 0 and (NH) (H) (r(t)(y(t) + p(t)y(t - τ))")" + q(t)G(y(t - α)) - h(t) H (y(t - β)) =f (t) are studied under the assumption ...[wzór] for various ranges of p(t). Using Schauder’s fixed point theorem, sufficient conditions are obtained for the existence of bounded positive solutions of (NH).
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