Periodic and subharmonic solutions for a 2$n$th-order $\phi_c$-Laplacian difference equation containing both advances and retardations

Peng Mei; Zhan Zhou; Genghong Lin

doi:10.3934/dcdss.2019134

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2019, Volume 12, Issue 7: 2085-2095. Doi: 10.3934/dcdss.2019134

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Periodic and subharmonic solutions for a 2$n$th-order $\phi_c$-Laplacian difference equation containing both advances and retardations

School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

* Corresponding author: Zhan Zhou
* Corresponding author: Zhan Zhou

Received: December 2017

Revised: May 2018

Published: June 2019

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Abstract

We consider a 2$n$th-order nonlinear difference equation containing both many advances and retardations with $\phi_c$-Laplacian. Using the critical point theory, we obtain some new and concrete criteria for the existence and multiplicity of periodic and subharmonic solutions in the more general case of the nonlinearity.

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Mathematics Subject Classification: 39A23.

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