DEPENDENCE OF EIGENVALUES ON THE PROBLEM

The eigenvalues of linear, regular, two point boundary value problems depend continuously on the problem. In the important self-adjoint case studied by NAIMARK and WEIDMANN this dependence is differentiable and the derivatives of the eigenvalues with respect to a given parameter: an endpoint, a boundary condition, a coefficient, or the weight funct ion, are found. Monotone properties of the eigenvalues with respect to the coefficients and the weight function are established without usin g the variational (min-max) characterization.