Abstract
The paper considers the Dirichlet problem for an elliptic functionaldifferential equation containing a combination of shifts and contractions of the argument of an unknown function under the Laplace operator. Sufficient conditions for unique solvability are established. It is also shown that the problem can have an infinite-dimensional variety of solutions. This work is done in the framework of the State Contract in accordance with the Additional Agreement No. 075-03-2020-239/2 from 07.07.2020, registry No. 248, Budgetary Classification Code 01104730290059611, for the project titled ‘Non-linear singular integro-differential equations and boundary value problems’. The authors also acknoowledge support by the Russian Foundation for Basic Research (project no. 18-41-200001p-a).
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