Finite time blow-up of semi-linear Klein-Gordon equations with positive initial energy in FLRW spacetimes

Blowing-up solutions for semi-linear Klein-Gordon equations are considered in Friedmann-Lemaître-Robertson-Walker spacetimes. Some sufficient conditions are shown by applying the concavity method for semi-linear wave equations in the Minkowski spacetime to semi-linear Klein-Gordon equations in FLRW spacetimes.