We consider an initial value problem of the K-dV equation. The initial function is, in our case, assumed to be periodic with respect to the x-coordinate. Such a periodic function is inserted as the potential function in the associated Schrödlinger equation. The equation is, therefore, of Hill's type. A stable region in the stability chart in the λ-A plane for Hill's equation corresponds to a band which consists of continuous eigenvalues, were A is the amplitude of the periodic function and λ the eigenvalue. As the potential function, we consider a function in which dips of cosine functions of one-period stand side by with constant interval. When the interval between two consecutive cosine pulses is made infinite, the eigenvalues for one potential of cosine type is obtained. In this limiting case, clear correspondence between the numbers of eigenvalues and solitons is obtained, and soliton regions are precisely determined. This analysis can be compared with results of computer experiments on the K-dV equation. On basis of our method, it is seen that the determination of soliton region is also usable for the determination of the number of solitons.