Solvability of boundary value transmission problems by Green's function method

摘要

In this study we give a comprehensive treatment for a class B VP's together with transmission (impulsive, jump or interface) conditions at the one interior singular point. A self-adjoint linear operator R is defined in a suitable Hilbert space H such that the eigenvalues of such a problem coincide with those of R and showed that it has a compact resolvent. We construct fundamental solutions and discuss some properties of spectrum. Moreover, we obtain the representation of Green's function for the considered problem.