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Research Article | Open Access

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
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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.

Keywords

telegraph equationnontrivial doubly periodic solutionHilbert's metricEigenvalue theoryuniquenessexistencemultiplicity and asymptotic behavior

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Electronic Research Archive
Volume 30 Issue 3,
March 2022
Pages 1104-1125
DOI: 10.3934/era.2022059

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Cite this article:
Deng N, Feng M. New results of positive doubly periodic solutions to telegraph equations. Electronic Research Archive, 2022, 30(3): 1104-1125. https://doi.org/10.3934/era.2022059

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Received: 05 October 2021
Revised: 03 December 2021
Accepted: 03 December 2021
Published: 15 March 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)