Multiple periodic solutions for coupled asymptotically linear wave equations with variable coefficients

Jiayu Deng; Jianhua Liu; Shuguan Ji

doi:10.3934/dcds.2025059

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2025, Volume 45, Issue 11: 4324-4348. Doi: 10.3934/dcds.2025059

This issue Previous Article Dynamics of translations on maximal compact subgroups Next Article Bistable waves for two species competition systems in a periodic discrete habitat

Multiple periodic solutions for coupled asymptotically linear wave equations with variable coefficients

1.
School of Mathematics and Statistics and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, China
2.
School of Science, Changchun Univeristy, Changchun 130022, China

^*Corresponding author: Shuguan Ji
^*Corresponding author: Shuguan Ji

Received: September 2024

Revised: March 2025

Early access: May 7, 2025

Published online: May 7, 2025

This work is partially supported by NSFC Grants (nos. 12225103, 12071065 and 12426662), the National Key Research and Development Program of China (nos. 2020YFA0713602 and 2020YFC1808301) and the Science and Technology Research Project of the Education Department of Jilin Province (JJKH20250298BS).

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Abstract

In this paper, we study the existence of multiple periodic solutions for coupled asymptotically linear wave equations with variable coefficients under some Sturm-Liouville boundary conditions. Such a mathematical model arises naturally when two seismic waves propagate simultaneously in a nonisotropic medium. By a delicate analysis for the asymptotic character of the spectrum of the variable coefficients wave operator, we construct a suitable functional space and give a non-resonance condition, and then at least three nontrivial periodic solutions are obtained. The main tools are the variational methods and saddle point reduction technique. Finally, our result is applicable to the uncoupled wave equations.

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Mathematics Subject Classification: Primary: 35B10, 35L05; Secondary: 35A15.

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