On long time existence for small solutions of semi-linear Klein-Gordon equations on the torus (Q1042659)

The author studies the initial value problem to the equation \(v_{tt}-\Delta v+m^2v=F(x,v)\) on a torus. He proves existence of a unique solution to the problem for small smooth initial data and almost all positive \(m\) over a time interval larger than the interval determined by local existence theory. Moreover, boundedness of norms of smooth solutions in Hilbert spaces is presented.