Asymptotic Properties of Neutral Differential Equations with Variable Coefficients

The aim of this work is to study oscillatory behavior of solutions for even-order neutral nonlinear differential equations. By using the Riccati substitution, a new oscillation conditions is obtained which insures that all solutions to the studied equation are oscillatory. The obtained results complement the well-known oscillation results present in the literature. Some example are illustrated to show the applicability of the obtained results.

[1]  Osama Moaaz,et al.  On the asymptotic behavior of fourth-order functional differential equations , 2017, Advances in Difference Equations.

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

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

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

[5]  Ravi P. Agarwal,et al.  A new approach in the study of oscillatory behavior of even-order neutral delay differential equations , 2013, Appl. Math. Comput..

[6]  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..

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

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

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

[10]  G. Chatzarakis,et al.  Oscillatory and asymptotic behavior of advanced differential equations , 2020 .

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

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

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

[14]  Blanka Baculíková,et al.  Oscillation theorems for higher order neutral differential equations , 2012, Appl. Math. Comput..

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

[16]  Osama Moaaz,et al.  New Results for Oscillatory Behavior of Fourth-Order Differential Equations , 2020, Symmetry.

[17]  Omar Bazighifan,et al.  On the oscillation of certain fourth-order differential equations with p-Laplacian like operator , 2020, Appl. Math. Comput..

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

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

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

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

[22]  Lihua Liu,et al.  New oscillation criteria for second-order nonlinear neutral delay differential equations , 2009, J. Comput. Appl. Math..

[23]  Osama Moaaz,et al.  Oscillation Results for Higher Order Differential Equations , 2020, Axioms.

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

[25]  Anedda Claudia,et al.  Second-order boundary estimates for solutions to singular elliptic equations in borderline cases , 2011 .

[26]  O. Bazighifan.  Oscillatory applications of some fourth‐order differential equations , 2020, Mathematical Methods in the Applied Sciences.