Diophantine approximation, Bessel functions and radially symmetric periodic solutions of semilinear wave equations in a ball期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Diophantine approximation, Bessel functions and radially symmetric periodic solutions of semilinear wave equations in a ball

Authors:	J Berkovits J Mawhin

Institution:	Department of Mathematics, University of Oulu, Oulu, Finland ; Université Catholique de Louvain, Institut Mathématique, B-1348 Louvain-la-Neuve, Belgium

Abstract:	The aim of this paper is to consider the radially-symmetric periodic-Dirichlet problem on $0,T] \times B^na]$ for the equation $\begin{displaymath}u_{tt} - \Delta u = f(t,\vert x\vert,u),\end{displaymath}$ where $\Delta$ is the classical Laplacian operator, and denotes the open ball of center and radius in ${\mathbb R}^n.$ When $\alpha = a/T$ is a sufficiently large irrational with bounded partial quotients, we combine some number theory techniques with the asymptotic properties of the Bessel functions to show that is not an accumulation point of the spectrum of the linear part. This result is used to obtain existence conditions for the nonlinear problem.

Keywords:	Diophantine approximations Bessel functions wave equation periodic solutions

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