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November 2019, 12(7): 2085-2095. doi: 10.3934/dcdss.2019134
Periodic and subharmonic solutions for a 2$n$th-order $\phi_c$-Laplacian difference equation containing both advances and retardations
Peng Mei , Zhan Zhou , and Genghong Lin
School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
* Corresponding author: Zhan Zhou
Received December 2017 Revised May 2018 Published December 2018
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.
Keywords: Periodic and subharmonic solution, 2$n$th-order, nonlinear difference equation, $\phi_c$-Laplacian, critical point theory.
Mathematics Subject Classification: 39A23.
Citation: Peng Mei, Zhan Zhou, Genghong Lin. Periodic and subharmonic solutions for a 2$n$th-order $\phi_c$-Laplacian difference equation containing both advances and retardations. Discrete & Continuous Dynamical Systems - S, 2019, 12 (7) : 2085-2095. doi: 10.3934/dcdss.2019134
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Peng Mei Zhan Zhou Genghong Lin
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