On a Nonlocal Problem of the Bitsadze–Samarskii Type for an Elliptic Equation with Degeneration
Abstract
In this research, a nonlocal Bitsadze–Samarskii type problem is investigated for a degenerate elliptic equation in a vertical half-strip $$\Omega=\big{\{}{\left({x,y}\right):0<x<1,y>0}\big{\}}.$$ This problem relates the value of the unknown function on the right boundary to the value of the function at an interior point of the domain. The uniqueness of the solution to the problem is proven using the extremum principle, and the existence of a solution to the problem is established by the methods of separation of variables and integral equations. In this paper, we also studied the spectral properties of the Bitsadze–Samarskii type problem for an ordinary differential equation of the second order, obtained using the spectral method, found the eigenvalues, as well as the corresponding eigenfunctions, proved their completeness and basis property, and also investigated the adjoint problem.