Nonlinear wave equation with potential (Q5933596)

The author proves the existence of a unique global solution of the Cauchy problem for the equation \(u_{tt}-\triangle u+V(x)|u|^{p-1}u=0\) \((x\in \mathbb{R}^{n}\), \(t>0)\), where \(V(x)=|x-x_{0}|\) for \(n=3\), or \(V(x)>0\) for \(n>3\), and \(p\) is a subcritical or critical exponent. To prove it, she uses Satah-Struwe technique and proves weighted nonlinear estimates in Besov spaces.