Neutral differential equations with noncanonical operator: Oscillation behavior of solutions

The objective of this work is to study the oscillatory behavior of neutral differential equations with several delays. By using both Riccati substitution technique and comparison with delay equations of first-order, we establish new oscillation criteria. Our new criteria are simplifying and complementing some related results that have been published in the literature. Moreover, some examples are given to show the applicability of our results.

[1]  Fanwei Meng,et al.  Oscillation criteria for certain even order quasi-linear neutral differential equations with deviating arguments , 2007, Appl. Math. Comput..

[2]  O. Moaaz,et al.  Oscillation Theorems for Nonlinear Differential Equations of Fourth-Order , 2020, Mathematics.

[3]  B. Baculíková,et al.  On the oscillation of higher-order delay differential equations , 2012, Journal of Mathematical Sciences.

[4]  C. Philos,et al.  On the existence of nonoscillatory solutions tending to zero at ∞ for differential equations with positive delays , 1981 .

[5]  Zhiting Xu,et al.  Integral averaging technique and oscillation of certain even order delay differential equations , 2004 .

[6]  Ravi P. Agarwal,et al.  New results for oscillatory behavior of even-order half-linear delay differential equations , 2013, Appl. Math. Lett..

[7]  Jurang Yan,et al.  Oscillation behavior of even order neutral differential equations with variable coefficients , 2006, Appl. Math. Lett..

[8]  Poom Kumam,et al.  On the Oscillatory Behavior of a Class of Fourth-Order Nonlinear Differential Equation , 2020, Symmetry.

[9]  Ravi P. Agarwal,et al.  Oscillation Theory for Difference and Functional Differential Equations , 2000 .

[10]  I. T. Kiguradze,et al.  Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations , 1992 .

[11]  Tongxing Li,et al.  Analysis and explicit solvability of degenerate tensorial problems , 2018 .

[12]  Giuseppe Viglialoro,et al.  A singular elliptic problem related to the membrane equilibrium equations , 2013, Int. J. Comput. Math..

[13]  D. Baleanu,et al.  New Aspects for Non-Existence of Kneser Solutions of Neutral Differential Equations with Odd-Order , 2020, Mathematics.

[14]  V. Lakshmikantham,et al.  Oscillation Theory of Differential Equations With Deviating Arguments , 1987 .

[15]  Said R. Grace,et al.  Oscillation criteria for second‐order Emden–Fowler delay differential equations with a sublinear neutral term , 2020, Mathematische Nachrichten.

[16]  Danna Zhou,et al.  d. , 1840, Microbial pathogenesis.

[17]  Ravi P. Agarwal,et al.  Oscillation Criteria for Certain nth Order Differential Equations with Deviating Arguments , 2001 .

[18]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[19]  G. S. Ladde,et al.  Oscillation of even order delay differential equations , 1987 .

[20]  M. Marini,et al.  Fourth-Order Differential Equation with Deviating Argument , 2012 .

[21]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[22]  Osama Moaaz,et al.  New oscillation criteria for nonlinear delay differential equations of fourth-order , 2020, Appl. Math. Comput..

[23]  A. Zafer,et al.  Oscillation criteria for even order neutral differential equations , 1998 .

[24]  Yuri V. Rogovchenko,et al.  On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations , 2020, Appl. Math. Lett..

[25]  Yuri V. Rogovchenko,et al.  Asymptotic Behavior of Higher-Order Quasilinear Neutral Differential Equations , 2014 .

[26]  Yuri V. Rogovchenko,et al.  On asymptotic behavior of solutions to higher-order sublinear Emden-Fowler delay differential equations , 2017, Appl. Math. Lett..

[27]  O. Moaaz,et al.  Oscillation Criteria of Higher-order Neutral Differential Equations with Several Deviating Arguments , 2020, Mathematics.

[28]  Tongxing Li,et al.  Properties of solutions to porous medium problems with different sources and boundary conditions , 2018, Zeitschrift für angewandte Mathematik und Physik.

[29]  Martin Bohner,et al.  Fite–Hille–Wintner-type oscillation criteria for second-order half-linear dynamic equations with deviating arguments , 2017 .

[30]  Li Gao,et al.  Oscillation behavior of even-order nonlinear neutral differential equations with variable coefficients , 2010, Comput. Math. Appl..

[31]  Bo Sun,et al.  On the oscillation of higher-order half-linear delay differential equations , 2011, Appl. Math. Lett..

[32]  Samir H. Saker,et al.  Oscillation of Fourth-Order Delay Differential Equations , 2014 .

[33]  Yuri V. Rogovchenko,et al.  Oscillation criteria for even-order neutral differential equations , 2016, Appl. Math. Lett..

[34]  Chenghui Zhang,et al.  Oscillation of higher-order quasi-linear neutral differential equations , 2011 .