New Oscillation Criteria for Second-Order Neutral Delay Dynamic Equations with a Nonpositive Neutral Term on Time Scales

Document Type : Original Research Papers

Authors

Mathematics Dept., Faculty of Science, Benha Univ., Benha, Egypt

Abstract

n this paper, we investigate the oscillatory behavior of solutions of a class of second order nonlinear neutral delay dynamic
equations with nonpositive coefficient
[𝑟(𝑡)(𝑧Δ(𝑡))𝛼]Δ + 𝑞(𝑡)𝑥𝛽(𝛿(𝑡)) = 0,
where 𝛼 ≥ 𝛽 are ratios of odd positive integers and 𝑧(𝑡): = 𝑥(𝑡) - 𝑝(𝑡)𝑥(𝜏(𝑡)). The obtained result not only new but also
answered the question that introduced by Li [12].

Keywords