Homoclinic solutions of discrete $ p $-Laplacian equations containing both advance and retardation

Peng Mei; Zhan Zhou; Yuming Chen; Peng Mei; Zhan Zhou; Yuming Chen

doi:10.3934/era.2022112

Electronic Research Archive

2022, Volume 30, Issue 6: 2205-2219. doi: 10.3934/era.2022112

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Homoclinic solutions of discrete $ p $-Laplacian equations containing both advance and retardation

1.
School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China
2.
Guangzhou Center for Applied Mathematics, Guangzhou University, Guangzhou, 510006, China
3.
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada

Received: 11 September 2021 Revised: 12 December 2021 Accepted: 18 December 2021 Published: 21 April 2022

We consider a $ 2m $th-order nonlinear $ p $-Laplacian difference equation containing both advance and retardation. Using the critical point theory, we establish some new and weaker criteria on the existence of homoclinic solutions with mixed nonlinearities.
- homoclinic solution,
- $ p $-Laplacian,
- mixed nonlinearity,
- critical point theory
Citation: Peng Mei, Zhan Zhou, Yuming Chen. Homoclinic solutions of discrete $ p $-Laplacian equations containing both advance and retardation[J]. Electronic Research Archive, 2022, 30(6): 2205-2219. doi: 10.3934/era.2022112

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Abstract

We consider a $ 2m $th-order nonlinear $ p $-Laplacian difference equation containing both advance and retardation. Using the critical point theory, we establish some new and weaker criteria on the existence of homoclinic solutions with mixed nonlinearities.

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