[en] Solitary small-scale and long-lived magnetic structures observed on the solar photosphere, so-called facular knots, are investigated on the base of Solar Dynamics Observatory (SDO) data. The long-term variations of the magnetic field and the emission in UV-lines with periods in the range of 25–250 minutes are revealed in the facular knots. The statistically significant oscillatory modes for each object under the study are found by the Empirical Mode Decomposition (EMD) method. It is noted that, although the object keeps its structural identity, during all its lifetime, their parameters, such as the strength of magnetic field, area on the magnetograms and on the intensity maps, the intensities in white light and other quantities can vary significantly. These variations change the effective rigidity of the system (the response of the system to the external disturbances), and it change radically the character of oscillations. Quasi-periodic variations of the magnetic field of facular knots with periods from one to several hours can be interpreted as an specific eigen oscillations of the system as a whole, having a time-varying rigidity. A simple analytical model is proposed to describe the observed oscillations of the facular knots.