Asymptotic and oscillatory behavior of solutions of a class of second order differential equations with deviating arguments

AbstractThe asymptotic and oscillatory behavior of solutions of damped nonlinear second order differential equations with deviating arguments of the type (a(t) ψ(x(t)) ẋ(t)). + p(t)ẋ(t) + q(t) + q(t)f(x[g(t)]) = 0 (. = d/dt) is studied. Criteria for oscillation of all solutions when the damping coefficient “p” is of constant sign on [t0, ∞) are established. Results on the asymptotic and oscillatory behavior of solutions of the damped-forced equation (a(t)ψ(x(t))ẋ(t)). + p(t)ẋ(t) + q(t)f(x[g(t)]) = e(t), where q is allowed to change signs in [t0, ∞), are also presented. Some of the results of this paper extend, improve, and correlate a number of existing criteria

Yan’s oscillation theorem revisited

AbstractYan’s contribution [J. Yan, Oscillation theorems for second order linear differential equations with damping, Proc. Amer. Math. Soc. 98 (1986) 276–282] was an important breakthrough in the development of the Theory of Oscillation. This frequently cited paper has stimulated extensive investigations in the field. During the last decade, an integral oscillation technique has been developed to such an extent as to allow us to revisit Yan’s fundamental oscillation theorem and remove one of the conditions, leaving the other assumptions and the conclusion intact, thus enhancing this keystone result

Oscillation theorems for second order nonlinear functional differential equations with damping

AbstractNew oscillation criteria are given for a second order nonlinear functional differential equation (α(t)χ(t))′ + δp(t)χ′[σ(t)] − q(t)|χ[g(t)]|λ sgnχ[g(t)] = 0, where δ = ±1 and λ > 0

THEOREMS OF KIGURADZE-TYPE AND BELOHOREC-TYPE REVISITED ON TIME SCALES

This article concerns the oscillation of second-order nonlinear dynamic equations. By using generalized Riccati transformations, Kiguradzetype and Belohorec-type oscillation theorems are obtained on an arbitrary time scale. Our results cover those for differential equations and difference equations, and provide new oscillation criteria for irregular time scales. Some examples are given to illustrate our results

Oscillation Criteria for Second‐Order Neutral Damped Differential Equations with Delay Argument

The chapter is devoted to study the oscillation of all solutions to second‐order nonlinear neutral damped differential equations with delay argument. New oscillation criteria are obtained by employing a refinement of the generalized Riccati transformations and integral averaging techniques

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

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 theorems for second order nonlinear differential equations with deviating arguments

New oscillation criteria for the oscillatory behaviour of the differential (a(t)x·(t)) ·+p(t)x·(t)+q(t)f(x[g(t)])=0                ,( · =ddt) and (a(t)ψ(x(t))x·(t)) ·+p(t)x·(t)+q(t)f(x[g(t)])=0, are establishe