Boundary-value problem for an elliptic functional differential equation with dilation and rotation of arguments

The paper is devoted to the Dirichlet problem in a flat bounded domain for a linear second-order functional differential equation in the divergent form with dilation, contraction and rotation of the argument of the higher-order derivatives of the unknown function. We study the existence, the uniqueness and the smoothness of the generalized solution for all possible values of the coefficients and parameters of transformations in the equation.