546 research outputs found

    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

    Differential/Difference Equations

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    The study of oscillatory phenomena is an important part of the theory of differential equations. Oscillations naturally occur in virtually every area of applied science including, e.g., mechanics, electrical, radio engineering, and vibrotechnics. This Special Issue includes 19 high-quality papers with original research results in theoretical research, and recent progress in the study of applied problems in science and technology. This Special Issue brought together mathematicians with physicists, engineers, as well as other scientists. Topics covered in this issue: Oscillation theory; Differential/difference equations; Partial differential equations; Dynamical systems; Fractional calculus; Delays; Mathematical modeling and oscillations

    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 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

    Kamenev-Type Oscillation Criteria of Second-Order Nonlinear Dynamic Equations on Time Scales

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    Using functions from some function classes and a generalized Riccati technique, we establish Kamenev-type oscillation criteria for second-order nonlinear dynamic equations on time scales of the form (p(t)ψ(x(t))k∘xΔ(t))Δ+f(t,x(σ(t)))=0. Two examples are included to show the significance of the results
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