论文信息 - The distribution of zeros of oscillatory solutions for second order nonlinear neutral delay differential equations

The distribution of zeros of oscillatory solutions for second order nonlinear neutral delay differential equations

Abstract In this paper, the distance between adjacent zeros of oscillatory solutions for second order nonlinear neutral delay differential equations ( a ( t ) z ′ ( t ) ) ′ + q ( t ) f ( x ( t − σ ) ) = 0 , t ≥ t 0 , where z ( t ) = x ( t ) + p ( t ) x ( t − τ ) is investigated. By means of inequality techniques, specific function sequences and nonincreasing solutions for corresponding first order differential inequality, some new estimates for the distribution of zeros of oscillatory solutions have been presented, which have extended and improved some known results.

[1] Wang Zhicheng,et al. The distribution of zeroes of solutions of neutral equations , 1997 .

[2] Hassan A. El-Morshedy. On the distribution of zeros of solutions of first order delay differential equations , 2011 .

[3] Hassan A. El-Morshedy,et al. The distribution of zeros of all solutions of first order neutral differential equations , 2015, Appl. Math. Comput..

[4] G. Ladas,et al. Oscillation Theory of Delay Differential Equations: With Applications , 1992 .

[5] Samir H. Saker,et al. Distribution of zeros and disconjugacy of fourth order differential equations , 2016 .

[6] Ravi P. Agarwal,et al. Oscillation of functional differential equations , 2005, Math. Comput. Model..

[7] Zhiting Xu,et al. Oscillation criteria for second order quasilinear neutral delay differential equations , 2009, Appl. Math. Comput..

[8] Ravi P. Agarwal,et al. Oscillation of second-order Emden–Fowler neutral delay differential equations , 2014 .

[9] Zeev Nehari,et al. On the Zeros of Solutions of Second-Order Linear Differential Equations , 1954 .

[10] Zuzana Doslá,et al. Oscillation of third-order nonlinear neutral differential equations , 2016, Appl. Math. Lett..

[11] Li Gao,et al. Oscillation for Third-Order Nonlinear Delay Dynamic Equations on Time Scales , 2013 .