On Elliptic Pseudo-differential Equations with an Integral Condition in a Special Multidimensional Cone

In this paper, one considers a model pseudo-differential equation in five-dimensional space outside of a cone like multi-faced angle. Using the wave factorization of elliptic symbol one constructs a general solution of the equation, and it depends on one arbitrary function from corresponding Sobolev–Slobodetskii space. One adds a certain integral condition to the equation for unique identification of this function. One studies a solvability for this problem when certain parameters of the cone tend to their limit values.