Multitransition solutions for a generalized Frenkel-Kontorova model

Wen-Long Li; Xiaojun Cui

doi:10.3934/dcds.2020273

Article Contents

2020, Volume 40, Issue 11: 6135-6158. Doi: 10.3934/dcds.2020273

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Multitransition solutions for a generalized Frenkel-Kontorova model

Wen-Long Li^1, , and
Xiaojun Cui^2,

1.
School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
2.
Department of Mathematics, Nanjing University, Nanjing 210093, China

^* Corresponding author: Wen-Long Li
^* Corresponding author: Wen-Long Li

Received: September 2019

Revised: May 2020

Published online: November 2020

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Abstract

We study a generalized Frenkel-Kontorova model. Using minimal and Birkhoff solutions as building blocks, we construct a lot of homoclinic solutions and heteroclinic solutions for this generalized Frenkel-Kontorova model under gap conditions. These new solutions are not minimal and Birkhoff any more. We use constrained minimization method to prove our results.

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Mathematics Subject Classification: 70G75, 74G22, 74G35.

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References

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