A problem in which an undetermined parameter is involved in the coefficients of a differential equation and in which the solution of the differential equation, with associated boundary conditions, exists only for certain discrete values of the parameter, called eigenvalues (or characteristic values, sometimes principal values). An important example of a physical problem that leads to a characteristic-value problem is the determination of the modes and frequencies of a vibrating system. In this case the dependent variable of the differential equation represents the displacements of the system and the parameter represents the frequencies of vibration.