On the oscillation of bounded solutions of higher order nonlinear neutral delay differential equations with oscillating coefficients
El-sheikh, M., Soliman, A., Abdalla, M., Hassan, A. (2018). On the oscillation of bounded solutions of higher order nonlinear neutral delay differential equations with oscillating coefficients. EKB Journal Management System, 5(1), 44-51. doi: 10.21608/jbes.2018.369760
M. M. A. El-sheikh; A. A. Soliman; M. H. Abdalla; A. M. Hassan. "On the oscillation of bounded solutions of higher order nonlinear neutral delay differential equations with oscillating coefficients". EKB Journal Management System, 5, 1, 2018, 44-51. doi: 10.21608/jbes.2018.369760
El-sheikh, M., Soliman, A., Abdalla, M., Hassan, A. (2018). 'On the oscillation of bounded solutions of higher order nonlinear neutral delay differential equations with oscillating coefficients', EKB Journal Management System, 5(1), pp. 44-51. doi: 10.21608/jbes.2018.369760
El-sheikh, M., Soliman, A., Abdalla, M., Hassan, A. On the oscillation of bounded solutions of higher order nonlinear neutral delay differential equations with oscillating coefficients. EKB Journal Management System, 2018; 5(1): 44-51. doi: 10.21608/jbes.2018.369760

On the oscillation of bounded solutions of higher order nonlinear neutral delay differential equations with oscillating coefficients

Journal of Basic and Environmental Sciences
Volume 5, Issue 1, January 2018, Page 44-51  XML PDF (571.61 K)
Document Type: Original Article
DOI: 10.21608/jbes.2018.369760
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Authors
M. M. A. El-sheikh1; A. A. Soliman2; M. H. Abdalla1; A. M. Hassan2
1Department of Mathematics, Faculty of Science, Menoufia University, Shebeen EL-Koom, Egypt
2Department of Mathematics, Faculty of Science, Benha University, Benha-Kalubia 13518, Egypt
Abstract
In this paper, new sufficient conditions are established for the oscillation of all bounded solutions of higher order dynamic
equations 
[ ( )( ( )) ] ( ) ( ( ( ))) = 0 for [ , ) ,
0
1
   T
  
r t z t q t f x t t t
n


where 
z(t):= x(t)  p(t)x( (t))
and 
  0
is a constant. The obtained results extend and supplement certain known 
results in literature. .
Keywords
Oscillation; Higher order; Nonlinear dynamic equations; Riccati technique; Taylors formula
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