On the solvability of the Cauchy characteristic problem for a nonlinear equation with iterated wave operator in the principal part

We consider one multidimensional version of the Cauchy characteristic problem in the light cone of the future for a hyperbolic equation with power nonlinearity with iterated wave operator in the principal part. Depending on the exponent of nonlinearity and spatial dimension of equation, we investigate the problem on the nonexistence of global solutions of the Cauchy characteristic problem. The question on the local solvability of that problem is also considered.