Some New Oscillation Results for Fourth-Order Neutral Differential Equations with Delay Argument

The aim of this paper is to study the oscillatory properties of 4th-order neutral differential equations. We obtain some oscillation criteria for the equation by the theory of comparison. The obtained results improve well-known oscillation results in the literate. Symmetry plays an important role in determining the right way to study these equation. An example to illustrate the results is given.

[1]  Blanka Baculíková,et al.  Oscillation theorems for second-order nonlinear neutral differential equations , 2011, Comput. Math. Appl..

[2]  M. Ruggieri,et al.  An Improved Criterion for the Oscillation of Fourth-Order Differential Equations , 2020, Mathematics.

[3]  Osama Moaaz,et al.  Asymptotic and Oscillatory Behavior of Solutions of a Class of Higher Order Differential Equation , 2019, Symmetry.

[4]  Jozef Džurina,et al.  Properties of the third order trinomial differential equations with delay argument , 2009 .

[5]  Omar Bazighifan,et al.  An Approach for Studying Asymptotic Properties of Solutions of Neutral Differential Equations , 2020, Symmetry.

[6]  Osama Moaaz,et al.  Oscillation criteria for even-order neutral differential equations with distributed deviating arguments , 2019, Advances in Difference Equations.

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

[8]  Jianping Cai,et al.  Numerical Verification and Comparison of Error of Asymptotic Expansion Solution of the Duffing Equation , 2008 .

[9]  Hassan A. El-Morshedy,et al.  Oscillation Criteria for First Order Differential Equations with Non-Monotone Delays , 2020, Symmetry.

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

[11]  Simone Fiori Nonlinear damped oscillators on Riemannian manifolds: Numerical simulation , 2017, Commun. Nonlinear Sci. Numer. Simul..

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

[13]  Ravi P. Agarwal,et al.  Oscillation criteria for certain fourth order nonlinear functional differential equations , 2006, Math. Comput. Model..

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

[15]  Hijaz Ahmad,et al.  New Oscillation Criteria for Advanced Differential Equations of Fourth Order , 2020, Mathematics.

[16]  R. Koplatadze Specific properties of solutions of first order differential equations with several delay arguments , 2015 .

[17]  Clemente Cesarano,et al.  A Philos-Type Oscillation Criteria for Fourth-Order Neutral Differential Equations , 2020, Symmetry.

[18]  Osama Moaaz,et al.  A New Approach in the Study of Oscillation Criteria of Even-Order Neutral Differential Equations , 2020, Mathematics.

[19]  Higinio Ramos,et al.  On the asymptotic and oscillatory behavior of the solutions of a class of higher-order differential equations with middle term , 2020, Appl. Math. Lett..

[20]  Jozef Džurina,et al.  Comparison theorems for the third order trinomial differential equations with delay argument , 2009 .

[21]  P. Kumam,et al.  Oscillation Theorems for Advanced Differential Equations with p-Laplacian Like Operators , 2020 .

[22]  M. Postolache,et al.  Improved Conditions for Oscillation of Functional Nonlinear Differential Equations , 2020, Mathematics.

[23]  S. Furuichi,et al.  New Comparison Theorems for the Nth Order Neutral Differential Equations with Delay Inequalities , 2020, Mathematics.

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

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

[26]  Simone Fiori,et al.  Nonlinear damped oscillators on Riemannian manifolds: Fundamentals , 2016, J. Syst. Sci. Complex..

[27]  Said R. Grace,et al.  Oscillation theorems for nth-order differential equations with deviating arguments , 1984 .

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

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

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

[31]  O. Bazighifan Kamenev and Philos-types oscillation criteria for fourth-order neutral differential equations , 2020 .