New Results for Oscillatory Behavior of Fourth-Order Differential Equations

Our aim in the present paper is to employ the Riccatti transformation which differs from those reported in some literature and comparison principles with the second-order differential equations, to establish some new conditions for the oscillation of all solutions of fourth-order differential equations. Moreover, we establish some new criterion for oscillation by using an integral averages condition of Philos-type, also Hille and Nehari-type. Some examples are provided to illustrate the main results.

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

[2]  Pavel Řehák,et al.  How the constants in Hille-Nehari theorems depend on time scales , 2006 .

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

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

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

[6]  Clemente Cesarano,et al.  Some New Oscillation Criteria for Second Order Neutral Differential Equations with Delayed Arguments , 2019, Mathematics.

[7]  Zhiting Xu,et al.  Integral averaging technique and oscillation of certain even order delay differential equations , 2004 .

[8]  Clemente Cesarano,et al.  Oscillation of Fourth-Order Functional Differential Equations with Distributed Delay , 2019, Axioms.

[9]  A. R. El-Nabulsi,et al.  Non-Linear Dynamics with Non-Standard Lagrangians , 2013 .

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

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

[12]  Ravi P. Agarwal,et al.  Oscillation criteria for second-order retarded differential equations , 1997 .

[13]  Pratibhamoy Das.  An a posteriori based convergence analysis for a nonlinear singularly perturbed system of delay differential equations on an adaptive mesh , 2018, Numerical Algorithms.

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

[15]  Clemente Cesarano,et al.  Asymptotic Properties of Solutions of Fourth-Order Delay Differential Equations , 2019, Symmetry.

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

[17]  Irena Jadlovská,et al.  On the oscillation of fourth-order delay differential equations , 2019, Advances in Difference Equations.

[18]  Clemente Cesarano,et al.  Qualitative Behavior of Solutions of Second Order Differential Equations , 2019, Symmetry.

[19]  Osama Moaaz,et al.  New criteria for oscillation of nonlinear neutral differential equations , 2019 .

[20]  P. Das.  A higher order difference method for singularly perturbed parabolic partial differential equations , 2018 .

[21]  R. El-Nabulsi.  Gravitational Field as a Pressure Force from Logarithmic Lagrangians and Non-Standard Hamiltonians: The Case of Stellar Halo of Milky Way , 2018 .

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

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

[24]  Osama Moaaz,et al.  Oscillation criteria for a class of third order damped differential equations , 2018 .

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

[26]  M. Marini,et al.  Fourth-Order Differential Equation with Deviating Argument , 2012 .

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

[28]  R. El-Nabulsi.  Fourth-Order Ginzburg-Landau differential equation a la Fisher-Kolmogorov and quantum aspects of superconductivity , 2019 .