The periodic-Dirichlet problem for some semilinear wave equations (Q1188253)

Considering the equations of the following form (1) \(Lu+Nu=f\) in a Hilbert space \(H\), where \(L: \text{dom }L\subset H\to H\) is linear and selfadjoint, and \(N: H\to H\) is a possibly nonlinear operator, the authors prove the existence and uniqueness of the solution for (1), and then show the applications of these results to the periodic-Dirichlet problem for multi-dimensional semilinear wave equations of the form \(u_{tt}-\Delta u+g(u)=f(t,x)\) on rectangles in \(\mathbb{R}^ n\) with sides commensurable with the time period.