Journal of Applied Analysis 11 (2005), No. 1, 081--094
Copyright Heldermann Verlag 2005
Existence for some Quasilinear Elliptic Systems with Critical Growth Nonlinearity and L1 data
Nour Eddine Alaa
Faculté des Sciences et Techniques Gueliz, Dép. de Mathématiques et Informatique, B. P. 618, Marrakech, Morocco
alaa@fstg-marrakech.ac.ma
F. Maach
Faculté des Sciences et Techniques Gueliz, Dép. de Mathématiques et Informatique, B. P. 618, Marrakech, Morocco
Ilham Mounir
Université Cadi Ayyad, Faculté des Sciences Semlalia, Dép. de Mathématiques, Prince My Abdellah B. P. 511, Marrakech, Morocco
ilhamounir@ucam.ac.ma
We prove the existence of weak solutions for some quasilinear elliptic reaction-diffusion systems with Dirichlet boundary conditions and satisfying to the two main properties: the positivity of the solutions and the balance law. The nonlinearity we consider here has critical growth with respect to the gradient and the data are in L1.
Keywords: Elliptic, quasilinear, quadratic, weak solutions, L1 data.
MSC: 35J20, 35J25, 35J65, 45H15
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