Investigation of the impact of delayed damping on the asymptotic behavior of solutions to Emden–Fowler neutral differential equations

This paper examines the oscillatory behavior of solutions to Emden–Fowler neutral differential equations that incorporate a delayed damping term. To our knowledge, there are no prior results addressing the impact of delayed damping on the oscillatory behavior of neutral equations. We establish a new sufficient criterion to confirm that non-oscillatory solutions exhibit asymptotic behavior. Then, we refine and extend this criterion to include the ordinary case. Applying our results to an Euler-type equation shows that they are an extension and complement to the results reported in the literature.