# American Institute of Mathematical Sciences

June  2011, 4(3): 523-538. doi: 10.3934/dcdss.2011.4.523

## Complete abstract differential equations of elliptic type with general Robin boundary conditions, in UMD spaces

 1 Département de Mathématiques et Informatique, ENSET d'Oran, B.P 1523 Oran El M'Naouer, Algeria 2 Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna 3 Laboratoire de Mathématiques, U.F.R Sciences, et Techniques, Université du Havre, B.P 540, 76058 Le Havre Cedex 4 Laboratoire de Mathématiques Pures et Appliquées, Université de Mostaganem, 27000, Algeria

Received  May 2009 Revised  January 2010 Published  November 2010

In this paper we prove some new results concerning a complete abstract second-order differential equation with general Robin boundary conditions. The study is developped in UMD spaces and uses the celebrated Dore-Venni Theorem. We prove existence, uniqueness and maximal regularity of the strict solution. This work completes previous one [3] by authors; see also [11].
Citation: Mustapha Cheggag, Angelo Favini, Rabah Labbas, Stéphane Maingot, Ahmed Medeghri. Complete abstract differential equations of elliptic type with general Robin boundary conditions, in UMD spaces. Discrete & Continuous Dynamical Systems - S, 2011, 4 (3) : 523-538. doi: 10.3934/dcdss.2011.4.523
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