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Existence of Periodic Solutions for a Class of p-Laplacian Systems with Delay

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Abstract

The purpose of this article is to study the existence of periodic solutions for the p-Laplacian systems with delay

$$\begin{aligned} -(|z'(t)|^{p-2}z'(t))'= & {} f(t,z(t+\tau ),z(t),z(t-\tau )),\\ z(\tau )-z(-\tau )= & {} z'(\tau )-z'(-\tau )=0. \end{aligned}$$

Using the saddle point theorem and the linking theorem, some new existence theorems are obtained for second-order p-Laplacian systems with delay.

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Funding

This work was supported by NNSF of China (Grant Nos. 11801094, 62072119) and NNSF of Guangdong Province (Grant Nos. 2018A030313871 and 2023A1515010001 ).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, 510520, Guangdong, People’s Republic of China

    Chengjun Guo, Xinjie Ye & Junming Liu

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  1. Chengjun Guo
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  2. Xinjie Ye
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  3. Junming Liu
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The authors contributed equally to this paper. All authors read and approved the final manuscript.

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Correspondence to Junming Liu.

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Guo, C., Ye, X. & Liu, J. Existence of Periodic Solutions for a Class of p-Laplacian Systems with Delay. Mediterr. J. Math. 21, 86 (2024). https://doi.org/10.1007/s00009-024-02629-w

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  • DOI: https://doi.org/10.1007/s00009-024-02629-w

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