Diophantine approximation, Bessel functions and radially symmetric periodic solutions of semilinear wave equations in a ball (Q2750934)

The authors consider the radially symmetric periodic-Dirichlet problem on \([0,T]\times B^n[a]\) for the equation NEWLINE\[NEWLINEu_{tt}-\Delta u= f\bigl(t,|x|, u\bigr),NEWLINE\]NEWLINE where \(B^n[a]\) denotes the open ball in \(\mathbb{R}^n\) centered at the origin with radius \(a\) and \(T>0\). They show first that zero is not an accumulation point of the spectrum of the linear part when \(\alpha= a/T\) is a sufficiently large irrational number with bounded partial quotients. Using this result they then derive conditions for the existence of solutions for the nonlinear problem above. The results extend the previous ones obtained by J. Mawhin and P. J. McKenna.