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Oscillation criteria for differential equation \(y^{(4)}+P(t)y''+R(t)y'+Q(t)y=0\). (English) Zbl 0598.34028
This paper is concerned with the oscillation of the differential equation \[ (R)\quad y^{(4)}+P(t)y''+R(t)y'+Q(t)y=0, \] where P(t), R(t), Q(t) are real-valued continuous functions on the interval \(I=<a,\infty)\), \(- \infty <a<\infty\). We assume throughout that (B) P(t)\(\leq 0\), R(t)\(\leq 0\), \(R^ 2(t)\leq 2P(t)Q(t)\) or (C) P(t)\(\leq R(t)\leq 0\), 2Q(t)\(\leq R(t)\) for all \(t\in I\) and Q(t) not identically zero in any subinterval of I. One can verify easily that (C) implies (B). Oscillation theorems and criteria for equation (R) are proved.

MSC:
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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References:
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