Oscillation of Emden–Fowler-Type Neutral Delay Differential Equations

Shyam Sundar Santra,Omar Bazighifan,Taher A Nofal,Hammad Alotaibi

doi:10.3390/axioms9040136

Shyam Sundar Santra, Omar Bazighifan + Show 2 more

Open Access

https://doi.org/10.3390/axioms9040136

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Abstract

In this work, we consider a type of second-order functional differential equations and establish qualitative properties of their solutions. These new results complement and improve a number of results reported in the literature. Finally, we provide an example that illustrates our results.

Highlights

They obtained sufficient conditions for the oscillation of the solutions of (1), using comparison techniques
Consider the class of Emden–Fowler-type neutral delay differential equations of the form: f (y)(u0 (y))c+ h(y)w a (ς(y)) = 0 for y ≥ y0 > 0, (1)where u(y) = w(y) + g(y)w(θ (y)) and c and a are the ratios of two odd positive integers
Where u(y) = w(y) + g(y)w(θ (y)) and c and a are the ratios of two odd positive integers

Summary

Introduction

They obtained sufficient conditions for the oscillation of the solutions of (1), using comparison techniques. Baculikova and Džurina [3] considered (1) and established sufficient conditions for the oscillation of the solutions of (1) under the assumptions Bohner et al [4] established sufficient conditions for the oscillation of the solutions of (1) when c = a and assuming limy→∞ Λ(y) < ∞ and 0 ≤ g(y) < 1. Chatzarakis et al [5] established sufficient conditions for the oscillation and asymptotic behavior of all solutions of second-order half-linear differential equations of the form: f (y)(w0 (y)) a

Results

Conclusion