On the Existence or Absence of Global Solutions for the Multidimensional Version of the Second Darboux Problem for Some Nonlinear Hyperbolic Equations

摘要

Consider the nonlinear wave equation of the form Lu := (a~2u)/(at~2)-Δu+mu=f(u)+f, (1) where f and F are given real functions, f is nonlinear, and u is the unknown real function; m = const ≥ 0, Δ = ∑ ~n_(i=1) a~2/ax~2_i, and n > 2.