Abstract
This work is devoted to the study of the methods of solving the boundary value problem with transformed arguments.In the studied problems, the arguments are transformed by mapping the type of involution.Moreover, these mappings are used both in the equation and in the boundary conditions.The equation under consideration is a nonlocal analogue of the Poisson equation.The boundary conditions are specified as a relation between the value of the desired function in the upper semicircle and its value in the lower semicircle.Two types of boundary conditions are considered.They generalize the known periodic and antiperiodic conditions for circular regions.When solving the main problems for the classical Poisson equation, auxiliary problems are obtained.Using well-known assertions for these auxiliary problems, theorems on the existence and uniqueness of solutions are proved.Exact conditions for the solvability of the studied problems are found.