We consider the boundary value problem generated on the finite closed interval x 0, 1 by the 2 2 system of ordinary differential equations y' - B (x) y= A (x) y, A (x) =diag\a₁ (x), a₂ (x) \, a₁ (x) < 0 < a₂ (x), and the boundary conditions U₀y (0) + U₁y (1) =0, where y (x) = (y₁ (x), y₂ (x) ) ^, U₀ and U₁ are constant (2 2) matrices, and the system coefficients aⱼ and b₉₊ are assumed to be absolutely continuous. In the regular case, we prove that the system of eigenfunctions and associated functions forms a Schauder basis in the space (Lₚ0, 1) ², and in the case of almost regular boundary value problem of order m N, we prove the Schauder basis property in some subspace of the space (W^m0, 1) ² with respect to the (Lₚ0, 1) ² -norm.
A. P. Kosarev (Mon,) studied this question.