A new result on the existence of periodic solutions for Rayleigh equation with a singularity

Guo, Yuanzhi; Wang, Yajiao; Zhou, Dongxue

doi:10.1186/s13662-017-1449-y

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Cited by 4 publications

(2 citation statements)

References 30 publications

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“…At the same time, Rayleigh equations with a singularity were also explored by authors [14,15,16,17,18,19,20,21]. For example, Lu et al [18] discussed p-Laplacian Rayleigh equations with a singularity in 2016 as follows:…”

Section: Introductionmentioning

confidence: 99%

Positive periodic solutions for a $\phi$-Laplacian generalized Rayleigh equation with a singularity

2023

J. Nonlinear Funct. Anal.

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Section: Introductionmentioning

confidence: 99%

Positive periodic solutions for a $\phi$-Laplacian generalized Rayleigh equation with a singularity

2023

J. Nonlinear Funct. Anal.

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“…Nowadays, a good deal of work has been performed on the existence of a positive periodic solution of the Rayleigh equation with a singularity [21][22][23][24]. Wang and Ma [24] in 2015 discussed a kind of singular Rayleigh equation as follows:…”

Section: Introductionmentioning

confidence: 99%

Singularity problems to fourth-order Rayleigh equation with time-dependent deviating argument

Xin

Liu

2018

Adv Differ Equ

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The paper is devoted to an investigation of the existence of a positive periodic solution for a kind of fourth-order singular Rayleigh equation with time-dependent deviating argument, where the nonlinear term g satisfies singularities of attractive and repulsive type at the origin and has time-dependent deviating argument. By applications of coincidence degree theory, we prove that this equation has at least one positive periodic solution. At last, two examples are given to show applications of theorems.

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New results on the existence of periodic solutions for Rayleigh equations with state-dependent delay

Eswari

Alzabut

Samei

et al. 2022

Nonautonomous Dynamical Systems

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We consider a Rayleigh-type equation with state–dependent delay ℘ ″ ( ϑ ) + 𝒱 1 ( ϑ , ℘ ( ϑ ) ) + A ( ℘ ( ϑ − 𝒱 2 ( ϑ , ℘ ( ϑ ) ) ) ) = B ( ϑ ) . \wp ''\left( \vartheta \right) + \mathcal{V}{_1}\left( {\vartheta ,\wp \left( \vartheta \right)} \right) + A\left( {\wp \left( {\vartheta - \mathcal{V}{_2}\left( {\vartheta ,\wp \left( \vartheta \right)} \right)} \right)} \right) = B\left( \vartheta \right). We establish a set of new su˚cient conditions on the existence of at least one positive periodic solution by using the continuation theorem of coincidence degree theory. Our results not only provide a new approach but also generalize previous results. An example with graphical representations are presented to illustrate the results.

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A new result on the existence of periodic solutions for Rayleigh equation with a singularity

Cited by 4 publications

References 30 publications

Positive periodic solutions for a $\phi$-Laplacian generalized Rayleigh equation with a singularity

Positive periodic solutions for a $\phi$-Laplacian generalized Rayleigh equation with a singularity

Singularity problems to fourth-order Rayleigh equation with time-dependent deviating argument

New results on the existence of periodic solutions for Rayleigh equations with state-dependent delay

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