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Oscillation and asymptotic analysis on a new generalized Emden-Fowler equation. (English) Zbl 1308.34084

Summary: In this work, we analyze the new generalized Emden-Fowler equation with neutral type delays: \[ (r(t)| Z'(t)|^{\alpha-1}Z'(t))'+q(t)| x(\sigma(t))|^{\beta-1}x(\sigma(t))=0, \] where \(Z(t)=x(t)+p(t)x(\tau(t))\), \(\alpha\geq\beta>0\). By use of averaging technique and specific analytical skills, some easily-accessible oscillation and asymptotic criteria are established, which have extended the results in the cited literature.

MSC:

34K11 Oscillation theory of functional-differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
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