Lifespan estimates for local solutions to the semilinear wave equation in Einstein–de Sitter spacetime

In this paper, we prove some blow-up results for the semilinear wave equation in generalized Einstein-de Sitter spacetime by using an iteration argument, and derive upper bound estimates lifespan. particular, will focus on critical cases which require employment of a slicing procedure iterative mechanism. Furthermore, order to deal with main case, introduce non-autonomous parameter-dependent Cauchy problem linear ODE second-order, whose explicit solution be determined applying theory special functions.