On solutions of the wave equation with a sublinear dissipative term (Q1109971)

The existence of periodic solution and a certain decay property for the nonlinear dissipative wave equation \[ u_{tt}-\Delta u+\sigma (u_ t)=f\quad in\quad R\times \Omega \quad (or\quad R^+\times \Omega) \] with the boundary condition \(u|_{\partial \Omega}=0\) are proved, where \(\Omega\) is a bounded domain in \(R^ n\) and \(\sigma\) (v) is a sublinear function, say, \(\sigma (v)=k_ 0| v|^{-r}v\), \(k_ 0>0\), \(0<r<1\).