Approximate method of solving Edwards' equation with nonrenormalizable interaction $\mathsf g^{\nu}(\ln\mathsf g)^{n_\nu}$

In the framework of an exactly solvable model with nonrenormalizable interaction (Edwards' equation) a method of differential interpolation is put forward and investigated; this enables one to construct series of a modified perturbation theory in powers of $g^{\nu}(\ln g)^{n_\nu}$, where $n_\nu$ is an integer and $\nu$ in the general case is not an integer. It is shown that the approximate solutions differ from the exact solutions only by finite terms.