On the oscillation of certain fourth-order differential equations with p-Laplacian like operator

Abstract The aim of this work is to study the oscillatory properties of the solutions of fourth-order delay differential equations with a p-Laplacian like operator of the form ( r ( ν ) | w ″ ′ ( ν ) | p 1 − 2 w ″ ′ ( ν ) ) ′ + q ( ν ) | w ( η ( ν ) ) | p 2 − 2 w ( η ( ν ) ) = 0 . The results obtained are based on the comparison with first and second-order differential equations and the use of a Riccati transformation. Some examples are provided to illustrate the main results.

[1]  Ravi P. Agarwal,et al.  Oscillation of fourth-order delay dynamic equations , 2015 .

[2]  Yuri V. Rogovchenko,et al.  Oscillation criteria for second-order superlinear Emden–Fowler neutral differential equations , 2017 .

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

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

[5]  Özkan Öcalan,et al.  COMPARISON THEOREMS ON THE OSCILLATION AND ASYMPTOTIC BEHAVIOUR OF HIGHER-ORDER NEUTRAL DIFFERENTIAL EQUATIONS , 2009, Glasgow Mathematical Journal.

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

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

[8]  C. Philos,et al.  Oscillation theorems for linear differential equations of second order , 1989 .

[9]  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..

[10]  Ravi P. Agarwal,et al.  Oscillation and asymptotic behavior of higher-order delay differential equations with p-Laplacian like operators , 2014 .

[11]  Li Gao,et al.  Oscillation criteria for even-order half-linear functional differential equations with damping , 2011, Appl. Math. Lett..

[12]  Chenghui Zhang,et al.  Oscillation of fourth-order neutral differential equations with p-Laplacian like operators , 2014 .

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

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

[15]  George E. Chatzarakis,et al.  Oscillation Criteria for Third-Order Emden-Fowler Differential Equations with Unbounded Neutral Coefficients , 2019, Complex..

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

[17]  E. Hille,et al.  Non-oscillation theorems , 1948 .

[18]  Gunnar Aronsson,et al.  On Hele–Shaw flow of power-law fluids , 1992, European Journal of Applied Mathematics.

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

[20]  Osama Moaaz,et al.  Oscillation of higher-order differential equations with distributed delay , 2019, Journal of Inequalities and Applications.

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

[22]  Ravi P. Agarwal,et al.  Oscillation results for fourth-order nonlinear dynamic equations , 2012, Appl. Math. Lett..

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

[24]  A. K. Nandakumaran,et al.  Oscillation criteria for differential equations of second order , 2009 .

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

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

[27]  Ravi P. Agarwal,et al.  Oscillation theorems for fourth order functional differential equations , 2009 .

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

[29]  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..

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

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

[32]  O. Bazighifan,et al.  Riccati Technique and Asymptotic Behavior of Fourth-Order Advanced Differential Equations , 2020, Mathematics.

[33]  Ravi P. Agarwal,et al.  Some remarks on oscillation of second order neutral differential equations , 2016, Appl. Math. Comput..

[34]  T. Abdeljawad,et al.  Improved Approach for Studying Oscillatory Properties of Fourth-Order Advanced Differential Equations with p-Laplacian Like Operator , 2020 .

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

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

[37]  G. Leonov,et al.  Hidden attractors in dynamical systems , 2016 .

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