Abstract
In this paper, we study the oscillation problem of the follow- ing higher-order neutral differential equation with positive and negative coefficients and mixed arguments z (n) (t) +q1(t)jx(t 1)j 1 x(t 1) +q2(t)jx(t 2)j 1 x(t 2) = e(t); where t t0, z(t) = x(t) p(t)x(t ) with p(t) > 0, > 1 > > 0, , 1 and 2 are real numbers. Without imposing any restriction on , we establish several oscillation criteria for the above equation in two cases: (i) q1(t) 0, q2(t) > 0, 1 0 and 2 ; (ii) q1(t) 0, q2(t) < 0, 1 and 2 0. As an interesting application, our results can also be applied to the following higher-order differential equation with positive and negative coefficients and mixed arguments x (n) (t) +q1(t)jx(t 1)j 1 x(t 1) +q2(t)jx(t 2)j 1 x(t 2) = e(t): Two numerical examples are also given to illustrate the main results.
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