New Criteria for Oscillation of Half-Linear Differential Equations with p-Laplacian-like Operators

The oscillation of nonlinear differential equations is used in many applications of mathematical physics, biological and medical physics, engineering, aviation, complex networks, sociophysics and econophysics. The goal of this study is to create some new oscillation criteria for fourth-order differential equations with delay and advanced terms ( a 1 ( x ) ( w ‴ ( x ) ) n ) ′ + ∑ j = 1 r β j ( x ) w k ( γ j ( x ) ) = 0 , {({a}_{1}(x){({w}^{\prime\prime\prime }(x))}^{n})}^{^{\prime} }+\mathop{\sum }\limits_{j=1}^{r}{\beta }_{j}(x){w}^{k}({\gamma }_{j}(x))=0, and ( a 1 ( x ) ( w ‴ ( x ) ) n ) ′ + a 2 ( x ) h ( w ‴ ( x ) ) + β ( x ) f ( w ( γ ( x ) ) ) = 0 . {({a}_{1}(x){({w}^{\prime\prime\prime }(x))}^{n})}^{^{\prime} }+{a}_{2}(x)h({w}^{\prime\prime\prime }(x))+\beta (x)f(w(\gamma (x)))=0. The method is based on the use of the comparison technique and Riccati method to obtain these criteria. These conditions complement and extend some of the results published on this topic. Two examples are provided to prove the efficiency of the main results.

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Delay Differential Equations of Fourth-Order: Oscillation and Asymptotic Properties of Solutions

Bazighifan

Al-Kandari

Al-Ghafri³

et al. 2021

Symmetry

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In this work, by using the comparison method and Riccati transformation, we obtain some oscillation criteria of solutions of delay differential equations of fourth-order in canonical form. These criteria complement those results in the literature. We give two examples to illustrate the main results. Symmetry plays an essential role in determining the correct methods for solutions to differential equations.

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New Criteria for Oscillation of Half-Linear Differential Equations with p-Laplacian-like Operators

Cited by 4 publications

References 26 publications

On the Oscillation of Solutions of Differential Equations with Neutral Term

On the Oscillation of Solutions of Differential Equations with Neutral Term

On the oscillation of nonlinear delay differential equations and their applications

Delay Differential Equations of Fourth-Order: Oscillation and Asymptotic Properties of Solutions

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