Fredholmness of an abstract differential equation of elliptic type

A. Aibeche, Universite Ferhat Abbes, Setif, Algeria

E. J. Qualitative Theory of Diff. Equ., No. 13. (2004), pp. 1-12.

Abstract: In this work, we obtain algebraic conditions which assure the Fredholm solvability of an abstract differential equation of elliptic type. In this respect, our work can be considered as an extension of Yakubov's results to the case of boundary conditions containing a linear operator. Although essential technical, this extension is not straight forward as we show it below. The obtained abstract result is applied to a non regular boundary value problem for a second order partial differential equation of an elliptic type in a cylindrical domain. It is interesting to note that the problems considered in cylindrical domains are not coercive.

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