A discussion on the continuous wavelet transform and differential equations in vector function spaces

In order to discuss differential equations of vector functions the continuous wavelet transform on the vector space is applied to the discussion of the relation between some differential equations of vector functions and the integral equations. The differential equations of vector functions can be transformed to the integral equations by using the continuous wavelet transform on the vector space. It is found that the differential equations are equivalent to the integral equations not only in the weak topology but also in the strong topology. The discussion on the differential equations can be associated with the discussion on the integral equations, which makes the continuous wavelet transform on the vector space applicable in the discussion of the differential equations of vector functions.