Abstract
Sufficient conditions, involving limsup and liminf, for the oscillation of all solutions of differential equations with several not necessarily monotone deviating arguments and nonnegative coefficients are established. Corresponding differential equations of both delayed and advanced type are studied. We illustrate the results and the improvement over other known oscillation criteria by examples, numerically solved in MATLAB.
Highlights
Consider the differential equations with several variable deviating arguments of either delayed m x (t) + pi(t)x τi(t) = for all t ≥ t, (E) i=or advanced type m x (t) – qi(t)x σi(t) = for all t ≥ t, (E ) and lim t→∞ τi (t) = ∞, ≤ i ≤ m, ( . )
An equation is oscillatory if all its solutions oscillate
Λ P(t), and λ is the smaller root of the transcendental equation λ = eαλ
Summary
An equation is oscillatory if all its solutions oscillate. The problem of establishing sufficient conditions for the oscillation of all solutions of equations (E) or (E ) has been the subject of many investigations. In , Zhou [ ] proved that if σi(t) are nondecreasing, σi(t) – t ≤ σ , ≤ i ≤ m, and m lim inf t→∞
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