The boundary conditions are obtained for NS interface at the presence of arbitrary concentrations of nonmagnetic impurities. The current states in SNS junction are considered. The solution obtained for the current is analysed, in particular it was found out how the characteristic length of the current decreasing ξ 0 for pure superconductor turns to ξ d for dirty one. A variant of the variational method, called the method of quasiorthogonality to asymptotics, is used to obtain the boundary conditions.

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A new integral equation that describes the behavior of the momentum space wave function for the one-dimensional Coulomb potential is proposed. The obtained result turned out to be a homogeneous Fredholm integral equation of the second kind and a singular integral equation, because its kernel has a singularity at some point in the momentum space. A nontriviality of the method of solving this singular integral equation lies in the application of the integral representation for its integral kernel. The technique applied in this paper made it possible to show that the wave function in the momentum representation is simultaneously a solution of the homogeneous Fredholm integral equation of the second kind and of the linear Volterra integral equation of the second kind. 
Since a linear Volterra integral equation of the second kind was easily transformed into a second order linear
inhomogeneous differential equation with constant coefficients, the eigenfunctions and eigenvalues in the one-dimensional Coulomb problem were found without any difficulties. Such a circumstance may indicate the validity of the new integral equation and the proposed method of its solving.

The behavior of the order parameter close to the NS interface in an SNINS junction is considered. To this end, a linear integral equation, which is valid near the superconductor-normal metal interface, is obtained and researched. The Ginzburg-Landau equation is solved taking into account the effect of the current on the space behaviour of the order parameter. Applying the method of quasiorthogonality to asymptotics, the boundary condition for the Ginzburg-Landau equation is obtained. The calculation of the current states, which can exist in an SNINS junction is carried out. We assume the normal layer thickness to be arbitrary and the temperature to be close to critical.

The equilibrium current states in superconducting junctions of the superconductor-insulator-superconductor (SIS) type were studied for arbitrary transparency of the dielectric layer and in the presence of nonmagnetic impurities of arbitrary concentration. As the study was carried out at temperatures close to critical, the Ginzburg–Landau theory was applied. The calculations were performed taking into account depairing effects, the presence of which in the system is reflected by the superfluid velocity term in the Ginzburg–Landau equation. In addition to the numerical results presented in the work, a new analytical equation for the dependence of the current on the phase difference was obtained for arbitrary electron transmittance and different values of the electron mean free path. It was shown that the analytical results are in good agreement with the numerical calculations.