Oscillatory behavior of the second order noncanonical differential equations

Establishing monotonical properties of nonoscillatory solutions we introduce new oscillatory criteria for the second order noncanonical differential equation with delay/advanced argument (r(t)y 0 (t))0 + p(t)y(τ(t)) = 0. Our oscillatory results essentially extend the earlier ones. The progress is illustrated via Euler differential equation

Oscillatory behavior of the second order noncanonical differential equations

Establishing monotonical properties of nonoscillatory solutions we introduce new oscillatory criteria for the second order noncanonical differential equation with delay/advanced argument (r(t)y 0 (t))0 + p(t)y(τ(t)) = 0. Our oscillatory results essentially extend the earlier ones. The progress is illustrated via Euler differential equation

Oscillation of Noncanonical Second-Order Advanced Differential Equations via Canonical Transform

In this paper, we develop a new technique to deduce oscillation of a second-order noncanonical advanced differential equation by using established criteria for second-order canonical advanced differential equations. We illustrate our results by presenting two examples

On nonoscillation of canonical or noncanonical disconjugate functional equations

summary:Qualitative comparison of the nonoscillatory behavior of the equations $$L_ny(t) + H(t,y(t)) = 0$$ and $$L_ny(t) + H(t,y(g(t))) = 0$$ is sought by way of finding different nonoscillation criteria for the above equations. $L_n$ is a disconjugate operator of the form $$L_n = \frac{1}{p_n(t)} \frac{\mathrm{d}{}}{\mathrm{d}t} \frac{1}{p_{n-1}(t)} \frac{\mathrm{d}{}}{\mathrm{d}t} \ldots \frac{\mathrm{d}{}}{\mathrm{d}t} \frac{\cdot }{p_0(t)}.$$ Both canonical and noncanonical forms of $L_n$ have been studied

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

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

An Improved Oscillation Result for a Class of Higher Order Non-canonical Delay Differential Equations.

[EN]In this work, by obtaining a new condition that excludes a class of positive solutions of a type of higher order delay differential equations, we were able to construct an oscillation criterion that simplifies, improves and complements the previous results in the literature. The adopted approach extends those commonly used in the study of second-order equations. The simplification lies in obtaining an oscillation criterion with two conditions, unlike the previous results, which required at least three conditions. In addition, we illustrate the improvement with the new criterion, applying it to some examples and comparing the results obtained with previous results in the literature

New monotonicity properties and oscillation of n-order functional differential equations with deviating argument

In this paper, we offer new technique for investigation of the even order linear differential equations of the form y (n) (t) = p(t)y(τ(t)). (E) We establish new criteria for bounded and unbounded oscillation of (E) which improve a number of related ones in the literature. Our approach essentially involves establishing stronger monotonicities for the positive solutions of (E) than those presented in known works. We illustrate the improvement over known results by applying and comparing our technique with the other known methods on the particular examples