International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

The spectral properties of the Sturm-Liouville operator whose potential is a first-order polynomial with coefficients that contain the involution operator are studied. The boundary conditions are not strong regular for Birkhoff. It is established that the operator of the problem contains in the system of root functions an infinite number of associated functions.The spectral properties of the operator of this problem are analyzed and the conditions for the existence and uniqueness of its solution are established. It is also proved that the system of root functions of the analyzed problem forms a Riesz basis.