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

Labbas R., Maingot S.

Demonstratio Mathematica

2003

Vol. 36, nr 3

627--652

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 Holder continuous functions. We prove that the solution can be represented explicitly as 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.

Resolution of a complete abstract second order differential equation of elliptic type

Labbas R., El Haial A.

Demonstratio Mathematica

1999

Vol. 32, nr 4

745-748

By application of function theoretic methods in partial differential equations (PDE), a nonlinear system of equations, elliptic in the sense of Lavrentiev with a linear boundary condition is investigated. Existence, uniqueness and stability for the boundary value problem (BVP) with degeneration of ellipticity have been proved.

On some Banach algebra of infinite matrices and applications

Labbas R., Malafosse B.

Demonstratio Mathematica

1998

Vol. 31, nr 1

153-168

We present in this work some new se