On the solvability of the Dirichlet problem for the nonlinear wave equation in bounded domains with corner points (Q1272322)

Using fixed point theory for non-expansive mappings and Mawhin's coincidence degree arguments the author studies the solvability of the Dirichlet problem for semilinear vibrating string equation \(u_{xx}-u_{yy}+ f(x,y,u)=0\) in a bounded domain \(\Omega\subset \mathbb{R}^2\) with corner points. The results are related to the rotation number associated to the domain.