When all solutions of \(x'=-\Sigma q_ i(t)x(t-T_ i(t))\) oscillate
This paper generalizes some results of \textit{G. Ladas, Y. G. Sficas} and \textit{I. P. Stavroulakis} concerning oscillatory solutions of the delay equation \(x'(t)=-\sum^{n}_{i=1}q_ ix(t-T_ i)\) [cf. Am. Math. Mon. 90, 637-640 (1983; Zbl 0526.34054)]. This paper considers delay equations of the form \(x'(t)=-\sum^{n}_{i=1}q_ i(t)x(t-T_ i(t))\) where \(T_ i\) and \(q_ i\) are continuous, positive functions on [0,\(\infty)\). The main result is that if there is a uniform upper bound \(T_ 0\) on the \(T_ i's\) and if the ''total torque'' \(\tau (t)=\sum^{n}_{i=1}q_ i(t)T_ i(t)\) satisfies \(\lim \inf_{t\to \infty} \tau (t)>1/e\) then all solutions of the above differential delay equation must oscillate.
scientific article; zbMATH DE number 3910836
scientific article