An Explicit Criterion for the Existence of Positive Solutions of the Linear Delayed Equation x˙(t)‎=−c(t)‎x(t−τ(t)‎)‎

Abstract EN

The paper investigates an equation with single delay ẋ(t)=-c(t)x(t-τ(t)), where τ:[t0-r,∞)→(0,r], r>0, t0∈R, and c:[t0-r,∞)→(0,∞) are continuous functions, and the difference t-τ(t) is an increasing function.

Its purpose is to derive a new explicit integral criterion for the existence of a positive solution in terms of c and τ.

An overview of known relevant criteria is provided, and relevant comparisons are also given.