Abstract
The main objective of this paper is to establish new oscillation results of solutions to a class of even-order advanced differential equations with a p-Laplacian like operator. The key idea of our approach is to use the Riccati transformation and the theory of comparison with first and second-order delay equations. Some examples are provided to illustrate the main results.
Highlights
We provide oscillation properties of even order advanced differential equation with a p-Laplacian like operator a (υ) y (κ −1) (υ) p −2 y j+ ∑ qi (υ) g (y (ηi (υ))) = 0, υ ≥ υ0, (1)i =1 where j ≥ 1, κ is even and p > 1 is a real number
We compare our result with the known related criteria for oscillation of this equation as follows: The condition q0 > 13.6 (6)
We compare our result with the known related criteria for oscillation of this equation as follows: (5)
Summary
We provide oscillation properties of even order advanced differential equation with a p-Laplacian like operator a (υ) y (κ −1). Where κ is an even and they established some new oscillation criteria by using the comparison technique Among others, they proved it oscillatory if lim inf υ→∞. The main aim of this paper is to establish new oscillation results of solutions to a class of even-order differential equations and they essentially complement and improve the results contained in [28,29,30].
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