On Solutions of Linear Elliptical Systems of Differential Equations with a Discontinuous Free Term
The author considers a non-homogeneous linear elliptical system of differential equations with smooth coefficients in the left part, but with an isolated point particularity of arbitrary (finite) order in the free term. The fundamental matrix, the existence of which is assumed, is modified in such a way that at the corresponding point, zero of the required order is formed. As a result the formula defining a certain partial solution of a non-homogeneous system, known for a smooth (or limited discontinuous) term, is extended to the case under discussion. Conclusions are drawn as to the statement and certain properties (generalized) of boundary problem solutions for such systems.
Citation Example: Gavelya S. P. On Solutions of Linear Elliptical Systems of Differential Equations with a Discontinuous Free Term // Ukr. Mat. Zh. - 1960. - 12, № 3. - pp. 235 - 243.