Explicit criteria for the oscillation of second-order differential equations with several sub-linear neutral coefficients

Shyam Sundar Santra,Tanusri Ghosh,Omar Bazighifan

doi:10.1186/s13662-020-03101-1

Abstract

In this work, we present sufficient conditions for oscillation of all solutions of a second-order functional differential equation. We consider two special cases when gamma >beta and gamma <beta . This new theorem complements and improves a number of results reported in the literature. Finally, we provide examples illustrating our results and state an open problem.

Highlights

1 Introduction Delay differential equations are widely used in mathematical modeling to describe physical and biological systems, often inducing oscillatory behavior [1,2,3,4, 8, 13, 14, 17, 18, 24,25,26, 28,29,30,31,32,33,34,35]
Numerous mathematical models with different levels of complexity have been proposed for delay differential equations in order to represent the cardiovascular system (CVS)
Ottesen [27] illustrated that complex dynamic interactions between nonlinear behaviors and delays associated with the autonomic-cardiac regulation may cause instability [5]

Summary

Introduction

Delay differential equations are widely used in mathematical modeling to describe physical and biological systems, often inducing oscillatory behavior [1,2,3,4, 8, 13, 14, 17, 18, 24,25,26, 28,29,30,31,32,33,34,35].In the literature, numerous mathematical models with different levels of complexity have been proposed for delay differential equations in order to represent the cardiovascular system (CVS).The pioneering and remarkable paper of Ottesen [27] shows how to use delay differential equations to solve a cardiovascular model that has a discontinuous derivative. In [36], Tripathy et al studied (3) and established several conditions of the solutions of (3) by considering the assumptions limt→∞ R(t) = ∞ and limt→∞ R(t) < ∞ for different ranges of the neutral coefficient p. In [9], Bohner et al obtained sufficient conditions for oscillation of solutions of (3) when γ = β, limt→∞ R(t) < ∞, and 0 ≤ p(t) < 1.

Results

Conclusion