The author deals with the semilinear differential equation
is any positive real number. In [Kyungpook Math. J. 28, No. 2, 119-122 (1988; Zbl 0709.34011
)] the author has proved the existence, uniqueness, and some properties of the solution of this equation when
. Here he mainly studies (besides the other properties) the continuation of the solution of this equation to the solution of the corresponding initial value problem when
. Applications of singular integro- differential equations are considered.