On Nonoscillation of Mixed Advanced-Delay Differential Equations with Positive and Negative Coefficients

TL;DR

This paper derives explicit conditions under which mixed advanced-delay differential equations with variable coefficients and delays do not oscillate, enhancing understanding of their stability properties.

Contribution

It provides new explicit nonoscillation criteria for mixed advanced-delay differential equations with variable delays and coefficients.

Findings

Established explicit nonoscillation conditions

Applicable to equations with variable delays and coefficients

Improves stability analysis of mixed differential equations

Abstract

For a mixed (advanced--delay) differential equation with variable delays and coefficients $$ \dot{x}(t) \pm a(t)x(g(t)) \mp b(t)x(h(t)) = 0, t\geq t_0 $$ where $$ a(t)\geq 0, b(t)\geq 0, g(t)\leq t, h(t)\geq t $$ explicit nonoscillation conditions are obtained.