turkmath.org

The questions of solvability and construction of solutions of a homogeneous nonlocal boundary value problem for a second-order homogeneous integro-differential Fredholm equation with a degenerate kernel and two real parameters are considered. The degenerate kernel method is developed. The features that have arisen in the construction of solutions and are associated with the determination of the integration coefficients are studied. The values of the real parameters are calculated, for which the solvability of the boundary value problem is established and the corresponding solutions are constructed.