eng Science and Education Publishing International Journal of Partial Differential Equations and Applications 2376-9556 2017-01-07 4 2 32 37 10.12691/ijpdea-4-2-3 IJPDEA2016423 article Samira Lecheheb 1 Hakim Lakhal m.maouni@univ-skikda.dz 1 Maouni Messaoud 1 Kamel Slimani 1 Université de Skikda, B.P.26 route d’El-Hadaiek, 21000, Algérie In this article, we are interested in the study of the existence of weak solutions of boundary value problem for the nonlinear elliptic system , where is a bounded domain in and are continuous functions . We use the Leray-Schauder degree theory under not linear for the three reasons: the terms of diffusion, convection and reaction, and the following condition on the last term f and and http://pubs.sciepub.com/ijpdea/4/2/3/ijpdea-4-2-3.pdf topological degree elliptic systems homotopy