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doi: 10.3934/cpaa.2021075
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On the even solutions of the Toda system: a degree argument approach

1. 

Department of Mathematics, University of Science and Technology of China, Hefei 230027, China

2. 

Department of Mathematics, Towson University, Towson, MD 21252, USA

3. 

School of Mathematical Sciences and Physics, North China Electric Power University, Beijing 102206, China

* Corresponding author

Dedicated to Professor Goong Chen on the occasion of his seventieth birthday

Received  November 2020 Revised  March 2021 Early access April 2021

Fund Project: Y. Liu is partially supported by "The Fundamental Research Funds for the Central Universities WK3470000014, " and NSFC no. 11971026. X. Yong is partially supported by the Beijing Natural Science Foundation no. Z200001

In this paper, we show the existence of even solutions with prescribed asymptotic behavior at infinity. Instead of using the integrability of the Toda system, the novel idea here is a degree argument approach. Perturbation theory has also been used in our study. Our method can be generalized to explore non-integrable systems with exponential type nonlinearities.

Citation: Yong Liu, Jing Tian, Xuelin Yong. On the even solutions of the Toda system: a degree argument approach. Communications on Pure & Applied Analysis, doi: 10.3934/cpaa.2021075
Figure 1.  A simple case of the two particles interactions
Figure 2.  A simple case of the three particles interactions
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