On the solution of a certain class of nonlinear singular integro-differential equations with Carleman shift

The solution of a class of nonlinear singular integro-differential equations with Carleman shift is obtained in the space Hμ(n)(Γ). The approach followed depends essentially on solution of linear singular integro-differential equation with shift. A criterion for the Noetherity of a correspondence singular integral functional operator of second order with Carleman shift preserving orientation is obtained and the index formula is given.