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Oscillation in first order neutral differential equations with ”integrally small” coefficients. (English) Zbl 0814.34062
The authors obtain some new sufficient conditions for the oscillation of the solutions of the equation (1) below without the restrictive hypothesis \(\int^{+\infty}_ 0 [P(s)- Q(s- \tau-\delta)] ds= +\infty\). \[ {d\over dt} [x(t)- R(t) x(t- r)]+ P(t) x(t- \tau)- Q(t) x(t-\delta)= 0,\tag{1} \] where \(P,Q,R\in C([t_ 0; +\infty),\mathbb{R}^ +)\), \(r> 0\) and \(\tau,\delta\geq 0\).

MSC:
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34K40 Neutral functional-differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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