Oscillation and asymptotic analysis on a new generalized Emden-Fowler equation

Abstract In this work, we analyze the new generalized Emden–Fowler equation with neutral type delays: r ( t ) | Z ′ ( t ) | α - 1 Z ′ ( t ) ′ + q ( t ) | x ( σ ( t ) ) | β - 1 x ( σ ( t ) ) = 0 , where Z ( t ) = x ( t ) + p ( t ) x ( τ ( t ) ) , α ⩾ β > 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.

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