On the even solutions of the Toda system: A degree argument approach

Yong Liu; Jing Tian; Xuelin Yong

doi:10.3934/cpaa.2021075

Article Contents

2022, Volume 21, Issue 6: 1895-1916. 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
^* Corresponding author

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

Received: October 31, 2020

Revised: February 28, 2021

Published: June 2022

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 34B30, 34D10, 34E99.

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Figure 1. A simple case of the two particles interactions

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Figure 2. A simple case of the three particles interactions

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