On Nonoscillation of Advanced Differential Equations with Several Terms

Abstract

Existence of positive solutions for advanced equations with several terms $\dot{x}\left(t\right)+{{\displaystyle \sum }}_{k=1}^m{a}_k\left(t\right)x\left(h_k\right(t\left)\right)=0$, $h_k\left(t\right)\ge t$ is investigated in the following three cases: (a) all coefficients $a_k$ are positive; (b) all coefficients $a_k$ are negative; (c) there is an equal number of positive and negative coefficients. Results on asymptotics of nonoscillatory solutions are also presented.