Université Ouaga I, Laboratoire LAMI, UFR Sciences Exactes et Appliquées, Département de Mathématiques, 03 BP 7021 Ouaga 03 Ouagadougou, Burkina Faso.
Received on September 12, 2016, revised version: December 20, 2016
Accepted on April 16, 2017
Communicated by Ahmed Nasir Uddin
Abstract. We study in this article the existence and uniqueness of a solution for nonlinear elliptic problemswith non-local boundary conditions. In order to get the unique solution, we study first an auxiliary problem, for which, we deduce useful a priori estimates. The study of the auxiliary problem give us equivalence between this kind of problem and nonlinear problem with very large diffusion around the boundary. | |
Keywords: | Non-local boundary conditions, Leray-Lions type operator, Operator of type M, Standard monotonicity arguments. |
2010 Mathematics Subject Classification: 35J05, 35J25, 35J60, 35J66. |