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This paper is concerned with oscillation of second-order nonlinear neutral dynamic equations on time scales with a variable delay. By using the generalized Riccati technique and integral averaging technique, new oscillation criteria are obtained for all solutions of the equation. Some results extend known results for difference equations when the time scale… (More)
In this paper, we first establish some differential inequalities and then some Sturm comparison theorems are derived for the second order nonlinear differential equations. Also, our results generalize some classical Sturm comparison theorems. 2004 Elsevier Inc. All rights reserved.
and Applied Analysis 3 Now one rewrites 1.1 as the following equivalent system ( x t px t − 1 )′ y1 t , 2.31 y′ 1 t y2 t , 2.32 .. .. y′ N−2 t yN−1 t , 2.3N−1 y′ N−1 t qx t f t . 2.3N 2.3 Let x t , y1 t , . . . , yN−1 t be solutions of system 2.3 on , for n ≤ t < n 1, n ∈ , using 2.3N we obtain yN−1 t yN−1 n qx n t − n ∫ t
We establish oscillation criteria for the second-order elliptic differential equation ∇ · (A(x)∇y) + B (x)∇y + q(x)f(y) = e(x), x ∈ Ω, where Ω is an exterior domain in RN . These criteria are different from most known ones in the sense that they are based on the information only on a sequence of annulus of Ω, rather than on the whole exterior domain Ω. Both… (More)
New oscillation criteria are established for the nonlinear matrix differential equations with a forced term [r(t)Y ′(t)]′ + p(t)Y ′(t) + Q(t)G(Y ′(t))F (Y (t)) = e(t)In. Our results extend and improve the recent results of Li and Agarwal for scalar cases. Furthermore, one example that dwell upon the importance of our results is included.
In this paper, we study the existence of almost periodic solutions of neutral differential difference equations with piecewise constant arguments via difference equation methods.