A class of non-analytic functions for the global solvability of Kirchhoff equation

We consider the global solvability to the Cauchy problem of Kirchhoff equation with generalized classes of Manfrins class. Manfrins class is a subclass of Sobolev space, but we shall extend this class as a subclass of the ultradifferentiable class, and we succeed to prove the global solvability of Kirchhoff equation with large data in wider classes from the previous works.