On solvability of some classes convolution type nonlinear multidimensional integral equations

The report is devoted to the problem of the solvability of certain classes of non-linear convolution type multidimensional integral equations . These classes of equations have direct applications in the theory of the geographical spread of the epidemic, in p-adic string theory. We prove constructive theorems for the existence of non-trivial and bounded solutions. The asymptotic behavior of the solutions is investigated. Specific examples of the equations in the above applications are given.