On the Strong Ellipticity of One Functional Differential Equation with Orthotropic Contraction in a Three-Dimensional Domain

In a three-dimensional domain containing the origin, we consider the first boundary value problem for a functional differential equation whose leading part contains orthotropic contraction transformations of the arguments of the unknown function. It is shown that the question of strong ellipticity, defined through a Gårding-type inequality, can be reduced to proving the positive definiteness of a self-adjoint difference operator with variable coefficients on a line. For the latter property, we provide some necessary and sufficient conditions in terms of the coefficients.