International Journal of Partial Differential Equations and Applications
ISSN (Print): 2376-9548 ISSN (Online): 2376-9556 Website: Editor-in-chief: Mahammad Nurmammadov
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International Journal of Partial Differential Equations and Applications. 2016, 4(2), 32-37
DOI: 10.12691/ijpdea-4-2-3
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Study of a System of Convection-Diffusion-Reaction

Samira Lecheheb1, Hakim Lakhal1, , Maouni Messaoud1 and Kamel Slimani1

1Université de Skikda, B.P.26 route d’El-Hadaiek, 21000, Algérie

Pub. Date: January 07, 2017

Cite this paper:
Samira Lecheheb, Hakim Lakhal, Maouni Messaoud and Kamel Slimani. Study of a System of Convection-Diffusion-Reaction. International Journal of Partial Differential Equations and Applications. 2016; 4(2):32-37. doi: 10.12691/ijpdea-4-2-3


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 Ω 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

topological degree elliptic systems homotopy

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[1]  A. Fattah, T. Gallouët, H. lakehal. An Existence proof for the stationary compressible stokes problem, Ann. Fac. Sci. de Toulouse Math. 6, 4 (2014), 847-875.
[2]  D. G. de Figueiredo. Semilinear elliptic systems. Lectures at the international school on nonlinear differential equations, Trieste-Italy, October (2006).
[3]  D. G. de Figueiredo, B. Ruf. Elliptic systems with nonlinearities of arbitrary growth, Mediterr, J. Math, 1 (2004), 417-431.
[4]  D. G. de Figueiredo, J. Yang. A priori bounds for positive solutions of a non-variational elliptic systems, Commun. Partial. Differ. Equations. 26 (2001), 2305-2321.
[5]  Th. Gallouet, O. Kavian. Résultats d’existence et de non-existence pour certains problèmes demilinéares à l’infini, Ann. Fac. Sci. de Toulouse Math. 5, 3 (1981), 201-246.
[6]  Th. Gallouet, O. Kavian. Resonace for jumping non-linearities, Journal of Partial Differential Equations. 7, 3 (1982), 325-342.
[7]  J. Kazdan, F.Waxusn; Remarks on some quasilinear elliptic equations, Comm. Pure. Appl. Math 28 (1975), 567-597.
[8]  O. Kavian. Introduction à la théorie des points critiques et Applications aux Problémes Elliptiques, Springer Verlag, Math. Appl, Vol 13, 1993.
[9]  H. Lakehal, B. Khodja, W. Gharbi. Existence results of nontrivial solutions for a semi linear elliptic system at resonance, Journal of Advanced Research in Dynamical and Control Systems Vol. 5, Issue. 3, 2013, pp. 1-12.
[10]  A. Moussaoui, B. Khodja. Existence results for a class of semilinear elliptic systems, Journal of Partial Differential Equations, 22 (2009), 111-126.
[11]  H. Lakhal, B. Khodja. Elliptic systems at resonance for jumping non- linearities, Electronic Journal of Differential Equations, Vol. 2016 (2016), No. 70, pp. 1-13.