On the Dirichlet Problem for an Elliptic Functional Differential Equation with Affine Transformations of the Argument

L. E. Rossovskii^a^,* and A. A. Tovsultanov^b^,**

^aRUDN University, Moscow, 117198 Russia

^bChechen State University, Grozny, 364024 Chechen Republic, Russia

Correspondence to: *e-mail: lrossovskii@gmail.com
Correspondence to: **e-mail: a.tovsultanov@mail.ru

Received 29 March, 2019

Abstract—The Dirichlet problem for an elliptic functional differential equation involving a shifted and contracted argument under the Laplacian sign is studied. Sufficient conditions for the unique solvability of the problem are established. It is shown that the problem may have an infinite-dimensional solution manifold.

DOI: 10.1134/S1064562419060140