Sufficient conditions for the existence of non-oscillatory solutions to first-order differential equations with multiple advanced arguments

Abstract

This article concerns the existence of non-oscillatory solutions to the equation $$ x'(t)=\sum_{k=1}^m a_k(t) x(h_k(t)), $$ where $a_k\geq 0$ and $h_k(t)\geq t$. We generalize existing results and then give an answer to the open question stated in [4]. Moreover we present a new condition based on the integral of $(\sum a_k)^2$.

Keywords

• Advanced linear differential equation
• positive solution
• oscillatory solution