Construction of a fundamental solution for a one degenerating elliptic equation with a Bessel operator

Degenerating elliptic equations containing the Bessel operator are mathematical models of axial and multi-axial symmetry of a wide variety of processes and phenomena of the surrounding world. Difficulties in the study of such equations are associated, inter alia, with the presence of singularities in the coefficients. This article considers a $p$-dimensional, $p\geqslant3,$ degenerating elliptic equation with a negative parameter, in which the Bessel operator acts on one of the variables. A fundamental solution of this equation is constructed and its properties are investigated, in particular, the behavior at infinity and at points of the coordinate planes $x_{p-1}=0,$ $x_p=0.$ The results obtained will find application in the construction of solutions of boundary value problems, since on the basis of a fundamental solution, it is possible to choose the potential with which the singular problem is reduced to a regular system of integral equations.