Oscillation for second order nonlinear differential equations with a sub-linear neutral term

We study the oscillatory behavior of solution to the second order nonlinear differential equations with a sub-linear neutral term $$ \big(a(t)[(x(t)+p(t)x^{\alpha}(\tau(t)))']^{\gamma}\big)'+q(t)x^{\beta}(\sigma(t))=0, \quad t\geq t_0>0. $$ A new criterion is established that improves related results reported in the literature. Moreover, some examples are provided to illustrate the main results.

[1]  George E. Chatzarakis,et al.  On the sharp oscillation criteria for half-linear second-order differential equations with several delay arguments , 2021, Appl. Math. Comput..

[2]  Jozef Dzurina,et al.  Kneser-type oscillation criteria for second-order half-linear delay differential equations , 2020, Appl. Math. Comput..

[3]  M. Bohner,et al.  Sharp oscillation criteria for second‐order neutral delay differential equations , 2020, Mathematical Methods in the Applied Sciences.

[4]  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..

[5]  Tongxing Li,et al.  Boundedness for a nonlocal reaction chemotaxis model even in the attraction-dominated regime , 2020, Differential and Integral Equations.

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

[7]  Tongxing Li,et al.  Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments , 2019, Mathematische Nachrichten.

[8]  S. Grace,et al.  An improved approach for studying oscillation of second-order neutral delay differential equations , 2018, Journal of inequalities and applications.

[9]  Zhenlai Han,et al.  New oscillation criterion for Emden–Fowler type nonlinear neutral delay differential equations , 2018, J. Appl. Math. Comput..

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

[11]  J. Graef,et al.  Oscillatory Behavior of second order nonlinear differential equations with a Sublinear neutral Term , 2018, Math. Model. Anal..

[12]  Jozef Dzurina,et al.  Oscillatory behavior of the second order noncanonical differential equations , 2017, Appl. Math. Lett..

[13]  Jozef Dzurina,et al.  A note on oscillation of second-order delay differential equations , 2017, Appl. Math. Lett..

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

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

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

[17]  Yuri V. Rogovchenko,et al.  Oscillation of second‐order neutral differential equations , 2015 .

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

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

[20]  Shurong Sun,et al.  Oscillation Theorems for Second-Order Quasilinear Neutral Functional Differential Equations , 2012 .

[21]  Chenghui Zhang,et al.  On the oscillation of second-order Emden-Fowler neutral differential equations , 2011 .

[22]  Qi-Ru Wang,et al.  Oscillation of second-order nonlinear neutral dynamic equations on time scales , 2010, Appl. Math. Comput..

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

[24]  J. Wong,et al.  On the Generalized Emden–Fowler Equation , 1975 .

[25]  M. Bohner,et al.  Oscillation criteria for second-order neutral delay differential equations , 2017 .

[26]  E. Thandapani,et al.  Oscillation of second order nonlinear differential equation with sub-linear neutral term , 2017 .

[27]  R. Agarwal,et al.  Oscillation of second-order differential equations with a sublinear neutral term , 2014 .