In this paper, the behavior and the properties of the generalized potential kernel (GPK) of the integral equations (IEs), in the axisymmetric contact and mixed problems, in the theory of elasticity are considered. Moreover, the behavior of the first and second structure of the GPK is discussed. Many special and new cases, from the kernel, are established. In addition, the behavior of the kernel of the first and second fundamental equations of an infinite elastic plate weakened by a curvilinear hole, in two-dimensional problems, in the theory of elasticity, is considered. The curvilinear hole is conformally mapped outside (inside) a unit circle, using a complex rational conformal mapping. Finally, the first and second structure properties of the complex kernel are proved.
