J. Nonl. Evol. Equ. Appl. 2017 (5), pp. 65-80, published on October 20, 2017:

Non-local boundary conditions for nonlinear elliptic problems with bounded data and general functions

S. Ouaro, S. Soma

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.

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