Existence of solution of a class of integral equation system

This paper proceeds according to following idea: whether an element has an image by inversion is equivalent to whether the mapping image set contains the element and equivalent to whether there exist solution of the mapping equation.If there are two mappings,and one set is larger than the other,in proper condition we can ascertain the difference of the two mappings contains a set,then original image of the set is not empty,and there exists a solution of the mapping equation of the difference.Applying the above idea to existence of solution of differential integral equation,we can obtain corresponding result.Applying the result to Hammerstein integral equation and Volterra integral equation,we obtain the result about existence of solution of these integral equations.We find our result is better than the results obtained by the partial ordering theory,fixed point index theory or iterative approximation theory.