Existence of infinitely many periodic solutions for the radially symmetric wave equation with resonance

Jianyi Chen,Zhitao Zhang

doi:10.1016/j.jde.2015.12.026

Existence of infinitely many periodic solutions for the radially symmetric wave equation with resonance

Jianyi Chen, Zhitao Zhang

Open Access

https://doi.org/10.1016/j.jde.2015.12.026

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Journal: Journal of Differential Equations	Publication Date: Dec 29, 2015
Citations: 17	License type: publisher-specific-oa

Affiliation: Qingdao Agricultural University, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

#N-dimensional Ball #Forced Wave Equation + Show 8 more

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Abstract

In this paper, we consider the periodic-Dirichlet problem for a forced nonlinear wave equation with resonance utt−Δu=μu+a(t,x)|u|p−1u in a n-dimensional ball. Under some suitable assumptions on μ, p and a(t,x), we prove the existence of infinitely many radially symmetric time-periodic solutions for the problem by variational methods.

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