1,173 research outputs found

    Oscillation Theorems for Second-Order Half-Linear Neutral Delay Dynamic Equations with Damping on Time Scales

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    We establish the oscillation criteria of Philos type for second-order half-linear neutral delay dynamic equations with damping on time scales by the generalized Riccati transformation and inequality technique. Our results are new even in the continuous and the discrete cases

    OSCILLATION OF SOLUTION TO SECOND-ORDER HALF-LINEAR DELAY DYNAMIC EQUATIONS ON TIME SCALES

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    This article concerns the oscillation of solutions to second-order half-linear dynamic equations with a variable delay. By using integral averaging techniques and generalized Riccati transformations, new oscillation criteria are obtained. Our results extend Kamenev-type, Philos-type and Li-type oscillation criteria. Several examples are given to illustrate our results

    Asymptotic Behavior of Even-Order Damped Differential Equations with p-Laplacian like Operators and Deviating Arguments

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    We study the asymptotic properties of the solutions of a class of even-order damped differential equations with p-Laplacian like operators, delayed and advanced arguments. We present new theorems that improve and complement related contributions reported in the literature. Several examples are provided to illustrate the practicability, maneuverability, and efficiency of the results obtained. An open problem is proposed

    Oscillation Results for Even Order Trinomial Functional Differential Equations with Damping

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    In this paper, we investigate the oscillatory behavior of solutions to a certain class of nonlinear functional differential equations of the even order with damping. By using the integral averaging technique and Riccati type transformations, we prove four new theorems on the subject. Several examples are also considered to illustrate the main results

    OSCILLATION of SECOND-ORDER HALF-LINEAR NEUTRAL NONCANONICAL DYNAMIC EQUATIONS

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    In This Paper, We Shall Establish Some New Criteria for the Oscillation of Certain Second-Order Noncanonical Dynamic Equations with a Sublinear Neutral Term. This Task is Accomplished by Reducing the Involved Nonlinear Dynamic Equation to a Second-Order Linear Dynamic Inequality. We Also Establish Some New Oscillation Theorems Involving Certain Integral Conditions. Three Examples, Illustrating Our Results, Are Presented. Our Results Generalize Results for Corresponding Differential and Difference Equations

    On the Oscillation for Second-Order Half-Linear Neutral Delay Dynamic Equations on Time Scales

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    We discuss oscillation criteria for second-order half-linear neutral delay dynamic equations on time scales by using the generalized Riccati transformation and the inequality technique. Under certain conditions, we establish four new oscillation criteria. Our results in this paper are new even for the cases of =ℝ and =ℤ

    On the Oscillation for Second-Order Half-Linear Neutral Delay Dynamic Equations on Time Scales

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    We discuss oscillation criteria for second-order half-linear neutral delay dynamic equations on time scales by using the generalized Riccati transformation and the inequality technique. Under certain conditions, we establish four new oscillation criteria. Our results in this paper are new even for the cases of T = R and T = Z
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