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# Existence of Multiple Periodic Solutions for a Semilinear Wave Equation in an n-Dimensional Ball

Hui Wei
• School of Mathematics and Statistics and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, P. R. China
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/ Shuguan Ji
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• School of Mathematics and Statistics and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024; and School of Mathematics, Jilin University, Changchun 130012, P. R. China
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Published Online: 2018-12-21 | DOI: https://doi.org/10.1515/ans-2018-2036

## Abstract

This paper is devoted to the study of periodic solutions for a radially symmetric semilinear wave equation in an n-dimensional ball. By combining the variational methods and saddle point reduction technique, we obtain the existence of at least three periodic solutions for arbitrary space dimension n. The structure of the spectrum of the linearized problem plays an essential role in the proof, and the construction of a suitable working space is devised to overcome the restriction of space dimension.

Keywords: Existence; Periodic Solutions; Wave Equation

MSC 2010: 35L71; 35B10

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Accepted: 2018-12-02

Published Online: 2018-12-21

Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11671071

Award identifier / Grant number: 11322105

Award identifier / Grant number: 11701077

Award identifier / Grant number: 11871140

Funding Source: Jilin University

Award identifier / Grant number: 2017TD–18

Funding Source: Department of Finance of Jilin Province

Award identifier / Grant number: 2017C028–1

This work is partially supported by NSFC Grants (nos. 11671071, 11322105, 11701077 and 11871140), the Fundamental Research Funds for the Central Universities at Jilin University (no. 2017TD–18) and the Special Funds of Provincial Industrial Innovation in Jilin Province (no. 2017C028–1).

Citation Information: Advanced Nonlinear Studies, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365,

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