Existence of Nonoscillation Solutions of Higher-Order Nonlinear Neutral Differential Equations | Asi

The following higher-order nonlinear neutral differential equations are considered in this paper: [x(t) + cx(t - )] dn dtn + (-1)n+1n+1n+1n+1n+1n+1n+1n [P(t)f1 (x(t - )) - Q(t)f2 (x(t - ))] [P(t)f1 (x(t - )) - Q(t)f2 (x(t - )) = 0; t t0; t t0; t t0; t t0; where ;; R+, c R; c=1, and P(t); Q(t) C([t0;; R+), fi(u) C(R; R), ufi(u) > 0. We obtain the results, which include some sufficient conditions for the presence of nonoscillation solutions, as well as a special case of the equation.

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