Abstract
Consider a retarded differential equation
and an advanced differential equation
wherea=m/n, m andn are odd natural numbers,P 0(t),P i(t) andg i(t) are continuous functions, andP i(t) are positive-valued on [t 0, ∞), limg i(t)=∞,i=1, 2, ...,N. We prove the following
Theorem. Suppose that there is a constantT such that
Then all solutions of (1) and (2) are oscillatory.
Here\(B_i = \mathop {\inf }\limits_{t \geqslant T} \int_{D_i } {P_0 (s)ds > - \infty } \) D i=[g i(t),t],T i(t)=t−g i(t), for (1), andD i=[t,g i(t)].T i(t)=g i(t)−t for (2),i=1, 2, ...,N.
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Yu, Y. Oscillations caused by several retarded and advanced arguments. Acta Mathematicae Applicatae Sinica 6, 67–73 (1990). https://doi.org/10.1007/BF02014717
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DOI: https://doi.org/10.1007/BF02014717