Note on oscillation conditions for first-order delay differential equations

Abstract

We consider explicit conditions for all solutions to linear scalar differential equations with several variable delays to be oscillatory. The considered conditions have the form of inequalities bounding the upper limit of the sum of integrals of coefficients over a subset of the real semiaxis, by the constant 1 from below. The main result is a new oscillation condition, which sharpens several known conditions of the kind. Some results are presented in the form of counterexamples.

Keywords

• differential equations
• delay
• oscillation
• sufficient conditions