SOLUTIONS OF SOME INTEGRAL EQUATIONS OF THE SECOND KIND

Abstract

The article examines the solutions of some integral equations of the second kind. Such equations arise when using Levi's method to construct a fundamental solution of the Cauchy problem for a degenerate equation of the Kolmogorov type. The equation may also contain a degeneracy on the initial hyperplane. The coefficients of this equation are bounded in the group of principal terms and ones are increasing functions in the group of lowest terms. The considered classes of kernels of integral equations make it possible to preserve the function that determines the growth of the coefficients of the parabolic equation when evaluating the resolvent. In the evalutions of the kernels of integral equations, there are evaluation functions that arise when constructing the corresponding fundamental solution, and fundamental solution of the Cauchy problem of the model equation with constant coefficients.