On the number of interior zeros of a one parameter family of solutions to a second order differential equation satisfying a boundary condition at one endpoint

AbstractA method for obtaining the existence of eigenvalues of an ordinary differential equation with separated boundary conditions is introduced. The method is based on counting the number of interior zeros of a one-parameter family of solutions which satisfy the boundary conditions at one of the end points. The coefficients of the differential equation depend continuously on the parameter but are not necessarily linear in the parameter