New results of positive doubly periodic solutions to telegraph equations

Nan Deng; Meiqiang Feng; Nan Deng; Meiqiang Feng

doi:10.3934/era.2022059

Electronic Research Archive

2022, Volume 30, Issue 3: 1104-1125. doi: 10.3934/era.2022059

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Research article

New results of positive doubly periodic solutions to telegraph equations

Nan Deng ,
Meiqiang Feng ^,

School of Applied Science, Beijing Information Science & Technology University, Beijing, 100192, China

Received: 05 October 2021 Revised: 03 December 2021 Accepted: 03 December 2021 Published: 11 March 2022

The paper is devoted to obtain new results of positive doubly periodic solutions to telegraph equations. One of the interesting features in our proof is that we give a new attempt to solve telegraph equation by using the theory of Hilbert's metric. Then we apply the eigenvalue theory to analyze the existence, multiplicity, nonexistence and asymptotic behavior of positive doubly periodic solutions. We also study a corresponding eigenvalue problem in a more general case.
- telegraph equation,
- nontrivial doubly periodic solution,
- Hilbert's metric,
- Eigenvalue theory,
- uniqueness,
- existence,
- multiplicity and asymptotic behavior
Citation: Nan Deng, Meiqiang Feng. New results of positive doubly periodic solutions to telegraph equations[J]. Electronic Research Archive, 2022, 30(3): 1104-1125. doi: 10.3934/era.2022059

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Abstract

The paper is devoted to obtain new results of positive doubly periodic solutions to telegraph equations. One of the interesting features in our proof is that we give a new attempt to solve telegraph equation by using the theory of Hilbert's metric. Then we apply the eigenvalue theory to analyze the existence, multiplicity, nonexistence and asymptotic behavior of positive doubly periodic solutions. We also study a corresponding eigenvalue problem in a more general case.

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