Stanislas Ouaro

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We study the structural stability (i.e., the continuous dependence on coefficients) of solutions of the elliptic problems under the form b(un)− div an(x,∇un) = fn. The equation is set in a bounded domain Ω of R and supplied with the homogeneous Dirichlet boundary condition on ∂Ω. Here b is a non-decreasing function on R, and (
* Correspondence: Laboratoire d’Analyse Mathématique des Equations (LAME) UFR. Sciences Exactes et Appliquées, Université de Ouagadougou 03 BP 7021 Ouaga 03, Ouagadougou, Burkina Faso Full list of author information is available at the end of the article Abstract In this article, we prove the existence and uniqueness of solutions for a family(More)
In this article we study the nonlinear homogeneous Neumann boundary-value problem b(u)− div a(x,∇u) = f in Ω a(x,∇u).η = 0 on ∂Ω, where Ω is a smooth bounded open domain in RN , N ≥ 3 and η the outer unit normal vector on ∂Ω. We prove the existence and uniqueness of a weak solution for f ∈ L∞(Ω) and the existence and uniqueness of an entropy solution for(More)
We study well-posedness for elliptic problems under the form b(u)− div a(x, u,∇u) = f, where a satisfies the classical Leray-Lions assumptions with an exponent p that may depend both on the space variable x and on the unknown solution u. A prototype case is the equation u− div ( | ∇u| ∇u ) = f . We have to assume that infx∈Ω, z∈R p(x, z) is greater than the(More)
where T ≥ 2 is a positive integer andΔu k u k 1 −u k is the forward difference operator. Throughout this paper, we denote by Z a, b the discrete interval {a, a 1, . . . , b}, where a and b are integers and a < b. We consider in 1.1 two different boundary conditions: a Dirichlet boundary condition u 0 0 and a Neumann boundary condition Δu T 0 . In the(More)
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