Global existence for solutions of \(\square u=A| u| ^ p\) (Q909323)

The author first proves a local existence theorem for the equation (1) \(\nabla^{\lambda}\nabla_{\lambda}u+au=b| u|^ p\), if \(1\leq p\leq n/(n-2)\) or \(p>[n/2]\), where \((V_ n\times {\mathbb{R}},9)\) is a globally hyperbolic manifold, and a and b given functions. The local existence theorem is then used to prove a global existence theorem valid for (1) if \(V_ n={\mathbb{R}}^ n\), the metric g is asymptotically minkowskian and a is asymptotically zero in a sufficiently strong sense.