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Oscillation of even order nonlinear functional differential equations with deviating arguments. (English) Zbl 0753.34047
Summary: Some new criteria for the oscillation of the differential equation \(x^{(n)}(t)+q(t)F(x[g(t)])=0\), \(n\) is even, are established. The obtained results unify, extend and improve a well-known sufficient condition for the oscillation of the so-called Emden-Fowler equation \[ x^{(n)}(t)+q(t)| x[g(t)]|^ \gamma\text{sgn} x[g(t)]=0, \] \(n\) is even, where \(\gamma\) is any positive constant.

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