A range of questions related to (i) the phase and magnetic dynamics of φ₀ Josephson junctions with ferromagnetic layers, (ii) Josephson junctions with controlled 0−π phase difference in the ground state, and (iii) the density of states in superconducting structures with the spatial inhomogeneity of the coupling constant of the Bardeen-Cooper-Schrieffer (BCS) theory are studied. The following results were obtained. (i) It is shown that in a φ₀ Josephson junction with a ferromagnet, under the action of an applied voltage, the easy axis of the ferromagnet is reoriented. Analytical criteria for the reversal of the magnetisation by a current pulse in φ₀ Josephson junctions of various types are also found. (ii) A new type of control for the phase difference 0−π of the ground state of Josephson junctions with the spin-orbit interaction in the leads is proposed. (iii) The form of the density of states of quasiparticles in superconductors with the spatial inhomogeneity of the BCS coupling constant is calculated.

(based on Ph.D. thesis)