In this work, we study an abstract boundary-value problem generated by an evolution equation and a non-local boundary condition. We prove the existence and uniqueness of the strong generalized solution and its continuity to respect to the parameters. The proofs are obtained via a priori estimates in non classical functional spaces and on the density of the range of the operator generated by the considered problem.
Submitted May 6, 2005. Published August 15, 2005.
Math Subject Classifications: 35F15, 35B45, 35R05, 34G10.
Key Words: Boundary-value problems; functional differential equations.
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| Assia Guezane-Lakoud |
Department of Mathematics
Faculty of Sciences, University Badji Mokhtar
B. P. 12, 23000, Annaba, Algeria
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