Asymptotics of three-dimensional integrals singularly depending on a small parameter

Asymptotics of some three-dimensional integrals singularly depending on a small parameter is constructed. The integrand denominator of the considered integrals is a sum of a small parameter and nonnegative function vanishing on three not intersecting surfaces. Such form integrals diverge as a small parameter tends to zero. The method of singularities subtraction and the circle method are applied.