A note on general oscillation for delay differential equations
The authors study delay differential equations of the form \[ y'(t)+\sum_{j=1}^na_jy(t-\tau_j)=0\;(t>0), \quad y(t)=\Phi(t)\;(-\tau\leq t\leq 0), \] with \(a_j\in\mathbb{R}\setminus\{0\}\), \(\tau_j\geq 0\) \((j=1,2,\dots,n)\), \(\Phi\in C[-\tau,0]\), and \(\tau=\max_{1\leq j\leq n}\tau_j\). It is a continuation of the article of the same authors [J. Math. Anal. Appl. 223, No. 1, 288-301 (1998; Zbl 0908.34055)]. Here, the existence of linear delay differential equations whose solutions are neither generically oscillatory nor generically nonoscillatory is demonstrated.
scientific article; zbMATH DE number 1375020