Investigation of the dimension of the spectral projection of a self-adjoint second order quasidifferential operator

Let λ 1 and λ 2 be real, λ 1 < λ 2 , functions ψ _( λ i , t ) be solutions to the second order quasidifferential equations L ψ _ = λ i P 0 ψ _ , i = 1, 2, satisfying a homogeneous boundary condition at point а . We express the number of eigenvalues of operator L , belonging to the interval (λ 1 , λ 2 ) (or the dimension of its spectral projection relative to the interval (λ 1 , λ 2 ), in terms of the number of zeros of the Vronskian composed for the functions ψ _(λ 1 , t ) and ψ _(λ 2 , t ).