Oscillation of a Class of Third-Order Neutral Differential Equations with Noncanonical Operators

The aim of this paper is to complement existing oscillation results for third-order neutral advanced differential equations under the condition of $$\gamma >0$$ γ > 0 ; in particular, the sufficient conditions are given in different way when $$\gamma =1$$ γ = 1 . Our main idea is by establishing sufficient conditions for nonexistence of so-called Kneser solutions. Then, combining with the results which guarantee the equation almost oscillation, we establish sufficient condition for oscillation of all solutions.

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

[2]  Tongxing Li,et al.  Oscillation of second-order neutral differential equations , 2015 .

[3]  Jozef Dzurina,et al.  Oscillation of third-order differential equations with noncanonical operators , 2018, Appl. Math. Comput..

[4]  William F. Trench,et al.  Canonical forms and principal systems for general disconjugate equations , 1974 .

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

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

[7]  Ravi P. Agarwal,et al.  Oscillation of second-order Emden–Fowler neutral delay differential equations , 2014 .

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

[9]  Chenghui Zhang,et al.  Oscillation of Third-Order Neutral Delay Differential Equations , 2012 .

[10]  Ravi P. Agarwal,et al.  OSCILLATION OF THIRD-ORDER NONLINEAR DELAY DIFFERENTIAL EQUATIONS , 2013 .

[11]  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..

[12]  Jozef Dzurina,et al.  On nonexistence of Kneser solutions of third-order neutral delay differential equations , 2019, Appl. Math. Lett..

[13]  R. Agarwal,et al.  Oscillation of Second-Order Nonlinear Neutral Dynamic Equations with Noncanonical Operators , 2015 .

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

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

[17]  G. Chang.  PWR advanced fuel high burnup-dependent xenon oscillation controllability assessment , 2019, Annals of Nuclear Energy.

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

[19]  Paul Van Houtte,et al.  Deformation texture prediction: from the Taylor model to the advanced Lamel model , 2005 .

[20]  Jan Dhaene,et al.  Probabilistic solutions for a class of deterministic optimal allocation problems , 2018, J. Comput. Appl. Math..