Singularities in boundary value problems for an abstract second-order differential equation of elliptic type

摘要

In this work we give an alternative approach to the study of some singular boundary value problems for a second order differential-operator equation in the space of Hölder continuous functions. We prove that the solution may be broken down explicitly into the sum u=uR+uS of a regular part and a singular part under some natural assumptions on the data. We then give a complete analysis of uR and uS by using the operational calculus.