Oscillation criteria for second order Emden-Fowler functional differential equations of neutral type

摘要

In this article, some new oscillation criterion for the second order Emden-Fowler functional differential equation of neutral type ( r ( t ) | z ′ ( t ) | α − 1 z ′ ( t ) ) ′ + q ( t ) | x ( σ ( t ) ) | β − 1 x ( σ ( t ) ) = 0 , $$igl(r(t)iglert z^{prime}(t)igrert ^{lpha-1}z^{prime}(t) igr)^{prime}+q(t)iglert xigl(sigma(t)igr)igrert ^{eta-1}x igl(sigma(t) igr)=0, $$ where z ( t ) = x ( t ) + p ( t ) x ( τ ( t ) ) $z(t)=x(t)+p(t)x(au(t))$ , α 0 $lpha0$ and β 0 $eta0$ are established. Our results improve some well-known results which were published recently in the literature. Some illustrating examples are also provided to show the importance of our results.