Journal of Mathematical Sciences

, Volume 197, Issue 1, pp 45–65

# Oscillation Criteria for Higher order Nonlinear Functional Differential Equations with Advanced Argument

Article
We consider a differential equation
$${u^{(n) }}(t)+p(t)\left| {u\left( {\sigma (t)} \right)\left| {^{{\mu (t)}}} \right.\mathrm{sign}\,u\left( {\sigma (t)} \right)=0,} \right.$$
where pL loc (R +; R +), μ ∈ C(R +; (0, +∞)), σ ∈ C(R +; R +), and σ(t) ≥ t for tR +. We say that the equation is almost linear if the condition lim t→+∞ μ(t) = 1 is satisfied. At the same time, if lim sup t→+∞ μ(t) ≠ 1 or lim inf t→+∞ μ(t) ≠ 1, then Eq. is called an essentially nonlinear differential equation. The oscillatory properties of almost linear differential equations have been extensively studied. In the paper, new sufficient (necessary and sufficient) conditions are established for a general class of essentially nonlinear functional differential equations to have Property A.

## Keywords

Differential Equation Satisfying Condition Nonlinear Differential Equation Linear Differential Equation Functional Differential Equation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

1. 1.Tbilisi State UniversityTbilisiGeorgia