On the Oscillation Criteria for Fourth-Order p -Laplacian Differential Equations with Middle Term

In this paper, we study the oscillatory properties of the solutions of a class of fourth-order p -Laplacian differential equations with middle term. The new oscillation criteria obtained by using the theory of comparison with first- and second-order differential equations and a refinement of the Riccati transformations. The results in this paper improve and generalize the corresponding results in the literatures. Three examples are provided to illustrate our results.

Oscillation of second-order nonlinear differential equations with damping

Mathematica Slovaca ◽

10.2478/s12175-014-0271-1 ◽

2014 ◽

Vol 64 (5) ◽

Author(s):

Tongxing Li ◽

Yuriy Rogovchenko ◽

Shuhong Tang

Keyword(s):

Differential Equations ◽

Nonlinear Differential Equations ◽

Nonlinear Damping ◽

Second Order ◽

Oscillation Criteria ◽

Nonlinear Anal ◽

AbstractWe study oscillatory properties of solutions to a class of nonlinear second-order differential equations with a nonlinear damping. New oscillation criteria extend those reported in [ROGOVCHENKO, Yu. V.—TUNCAY, F.: Oscillation criteria for second-order nonlinear differential equations with damping, Nonlinear Anal. 69 (2008), 208–221] and improve a number of related results.

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

Oscillation criteria for second order differential equations with damping

10.1017/s1446788700030226 ◽

1990 ◽

Vol 49 (1) ◽

pp. 43-54 ◽

Cited By ~ 17

Author(s):

S. R. Grace

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Second Order ◽

Linear Differential Equations ◽

Nonlinear Ordinary Differential Equations ◽

Oscillation Criteria ◽

Linear Differential

AbstractNew oscillation criteria are given for second order nonlinear ordinary differential equations with alternating coefficients. The results involve a condition obtained by Kamenev for linear differential equations. The obtained criterion for superlinear differential equations is a complement of the work established by Kwong and Wong, and Philos, for sublinear differential equations and by Yan for linear differential equations.

Interval oscillation criteria for certain forced second-order differential equations

Carpathian Journal of Mathematics ◽

10.37193/cjm.2012.02.01 ◽

2012 ◽

Vol 28 (2) ◽

pp. 337-344

Author(s):

ERCAN TUNC ◽

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Second Order ◽

Half Line ◽

Oscillation Criteria ◽

Interval Oscillation

By using generalized Riccati transformations and an inequality due to Hardy et al., several new interval oscillation criteria are established for the nonlinear damped differential equation... The new interval oscillation criteria are different from most known ones in the sense they are based on the information only on a sequence of subintervals of [t0, ∞), rather than on the whole half-line. Our results improve and extend the known some results in the literature.

Improved Conditions for Oscillation of Functional Nonlinear Differential Equations

Mathematics ◽

10.3390/math8040552 ◽

2020 ◽

Vol 8 (4) ◽

pp. 552 ◽

Cited By ~ 14

Author(s):

Omar Bazighifan ◽

Mihai Postolache

Keyword(s):

Differential Equations ◽

Fourth Order ◽

Delay Differential Equations ◽

Nonlinear Differential Equations ◽

Oscillation Criteria ◽

Delay Differential ◽

The aim of this work is to study oscillatory properties of a class of fourth-order delay differential equations. New oscillation criteria are obtained by using generalized Riccati transformations. This new theorem complements and improves a number of results reported in the literature. Some examples are provided to illustrate the main results.

Improved Approach for Studying Oscillatory Properties of Fourth-Order Advanced Differential Equations with p-Laplacian Like Operator

Mathematics ◽

10.3390/math8050656 ◽

2020 ◽

Vol 8 (5) ◽

pp. 656 ◽

Cited By ~ 12

Author(s):

Omar Bazighifan ◽

Thabet Abdeljawad

Keyword(s):

Differential Equations ◽

Fourth Order ◽

Delay Equations ◽

Riccati Transformation ◽

Oscillation Criteria ◽

First Order ◽

This paper aims to study the oscillatory properties of fourth-order advanced differential equations with p-Laplacian like operator. By using the technique of Riccati transformation and the theory of comparison with first-order delay equations, we will establish some new oscillation criteria for this equation. Some examples are considered to illustrate the main results.

Some New Oscillation Results for Fourth-Order Neutral Differential Equations with Delay Argument

Symmetry ◽

10.3390/sym12081248 ◽

2020 ◽

Vol 12 (8) ◽

pp. 1248 ◽

Cited By ~ 1

Author(s):

Omar Bazighifan ◽

Osama Moaaz ◽

Rami Ahmad El-Nabulsi ◽

Ali Muhib

Keyword(s):

Differential Equations ◽

Fourth Order ◽

Oscillation Criteria ◽

Neutral Differential Equations ◽

Delay Argument ◽

The Right ◽

Equations With Delay ◽

The aim of this paper is to study the oscillatory properties of 4th-order neutral differential equations. We obtain some oscillation criteria for the equation by the theory of comparison. The obtained results improve well-known oscillation results in the literate. Symmetry plays an important role in determining the right way to study these equation. An example to illustrate the results is given.