Strong Solvability of a Nonlocal Problem for the Laplace Equation in Weighted Grand Sobolev Spaces

We consider a nonlocal boundary value problem for the Laplace equation in an unbounded domain in Sobolev spaces generated by the norm of the weighted grand Lebesgue space. The notion of strong solvability of this problem is defined and its correct solvability is proved. At the same time, the basis property of one trigonometric system in separable weighted grand Lebesgue spaces is proved, and this fact is used to establish the correct solvability. Note that earlier this problem was considered by E.I.Moiseev [10] in the classical formulation.