Higher-order Nonlinear Dynamic Equations Research Articles

Asymptotics and oscillation for certain higher-order nonlinear dynamic equations on time scales

Asymptotics and oscillation for certain higher-order nonlinear dynamic equations on time scales

New Oscillation Criteria for Higher Order Nonlinear Dynamic Equations

AbstractThis paper deals with some new criteria for the oscillation of higher-order nonlinear dynamic equations with mixed deviating arguments. The purpose of the present paper is the linearization of the equation under consideration. Specifically, we will infer the oscillation of the studied equation from its linear form and establish new oscillation criteria by comparing it with first-order equations whose oscillatory behaviour is known. The obtained results are new, improve, and correlate many of the known oscillation criteria appearing in the literature. The results are illustrated by two examples.

Oscillation of higher order nonlinear dynamic equations with a nonlinear neutral term

This study introduces the oscillation of higher order nonlinear dynamic equations with a nonlinear neutral term. The findings are obtained via utilising an integral criterion as well as a comparison theorem with the oscillatory properties of a first‐order dynamic equation. We propose novel oscillation criteria that improve, extend and simplify existing ones in the literature. The results are associated with several numerical examples.

Some Oscillation Criteria for a Class of Higher Order Nonlinear Dynamic Equations with a Delay Argument on Time Scales

Some Oscillation Criteria for a Class of Higher Order Nonlinear Dynamic Equations with a Delay Argument on Time Scales

Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order

We will consider the higher order functional dynamic equations with mixed nonlinearities of the formxnt+∑j=0Npjtϕγjxφjt=0, on an above-unbounded time scaleT, wheren≥2,xi(t)≔ri(t)ϕαixi-1Δ(t),  i=1,…,n-1,   with  x0=x,  ϕβ(u)≔uβsgn⁡u, andα[i,j]≔αi⋯αj. The functionφi:T→Tis a rd-continuous function such thatlimt→∞φi(t)=∞forj=0,1,…,N. The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.

Oscillation criteria for higher order nonlinear dynamic equations

In this paper, we will consider the higher‐order functional dynamic equations of the form urn:x-wiley:dummy:mana201300157:equation:mana201300157-math-0001on an above‐unbounded time scale , where and , . The function is a rd‐continuous function such that . The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.

Oscillation of higher order nonlinear dynamic equations on time scales

Some new criteria for the oscillation of n th order nonlinear dynamic equations of the form

Asymptotic behaviors of higher order nonlinear dynamic equations on time scales

In this paper, we study asymptotic behaviour of solutions of the following higher order nonlinear dynamic equations $$y^{\triangle^n}(t)+\delta p(t)f(y(g(t)))=0$$ and $$y^{\triangle^n}(t)+\delta p(t)f(y(h(t)))=0$$ on an arbitrary time scale \(\mathbb{T}\) with \(\sup {\mathbb{T}}=\infty\), where n is a positive integer and δ=1 or −1. We obtain some sufficient conditions for the equivalence of the oscillation of the above equations.