Stanislas Ouaro

Weak solutions for anisotropic discrete boundary value problems

In this paper, we prove the existence and uniqueness of weak solutions for a family of discrete boundary value problems for data f which belong to a discrete Hilbert space H. Moreover, as an extension, we prove some existence results of weak solutions for more general data f depending on the solution.

Well-Posedness Results for Anisotropic Nonlinear Elliptic Equations with Variable Exponent and L¹-Data

Estudiamos el problema de valores en la frontera anisotropico en , u = 0 sobre , donde es un dominio abierto suave do . Proveamos la existencia y unicidad de una solucion de entropia para este problema.

On the solvability of discrete nonlinear Neumann problems involving the p(x)-Laplacian

AbstractIn this article, we prove the existence and uniqueness of solutions for a family of discrete boundary value problems for data f which belongs to a discrete Hilbert space W. 2010 Mathematics Subject Classification: 47A75; 35B38; 35P30; 34L05; 34L30.

Multivalued problem with Robin boundary condition involving diffuse measure data and variable exponent

Abstract We study a nonlinear elliptic problem with Robin type boundary condition, governed by a general Leray–Lions operator with variable exponents and diffuse Radon measure data which does not charge the sets of zero p(·)-capacity. We prove an existence and uniqueness result of a weak solution.

Stability analysis of a schistosomiasis model with delays

In this work, a nonlinear deterministic model for schistosomiasis transmission including delays with two general incidence functions is considered. Rigourous mathematical analysis is done. We show that the stability of the disease-free equilibrium and the existence of an endemic equilibrium for the model are stated in terms of key thresholds parameters known as basic reproduction number R0. This study of the dynamic of the model is globally asymptotically stable if R0≤1, and the unique endemic equilibrium is globally asymptotically stable when R0>1. Some numerical simulations are provided to support the theoretical result with respect to R0 in this paper.

On the Solvability of Discrete Nonlinear Two-Point Boundary Value Problems

We prove the existence and uniqueness of solutions for a family of discrete boundary value problems by using discretes Wirtinger inequality. The boundary condition is a combination of Dirichlet and Neumann boundary conditions.

Weak and entropy solutions to nonlinear Neumann boundary-value problems with variable exponents

In this article, we study the following nonlinear Neumann boundary-value problem − div a(x, ∇u) + |u| p(x)−2 u = f in Ω, on ∂Ω, where Ω is a smooth bounded open domain in ℝ N , is the outer unit normal derivative on ∂Ω, div a(x, ∇u) a p(x)-Laplace type operator. We prove the existence and uniqueness of a weak solution for f ∈ L (p −)′(Ω), the existence and uniqueness of an entropy solution for L 1-data f independent of u and the existence of weak solutions for f dependent on u. The functional setting involves Lebesgue and Sobolev spaces with variable exponents.

Weak homoclinic solutions of anisotropic difference equation with variable exponents

In this paper, we prove the existence of homoclinic solutions for a family of anisotropic difference equations. The proof of the main result is based on a minimization method and a discrete Hölder type inequality.MSC:47A75, 35B38, 35P30, 34L05, 34L30.

On the Global Dynamics of a Vector-Borne Disease Model with Age of Vaccination

We study a vector-borne disease with age of vaccination. A nonlinear incidence rate including mass action and saturating incidence as special cases is considered. The global dynamics of the equilibria are investigated and we show that if the basic reproduction number is less than 1, then the disease-free equilibrium is globally asymptotically stable; that is, the disease dies out, while if the basic reproduction number is larger than 1, then the endemic equilibrium is globally asymptotically stable, which means that the disease persists in the population. Using the basic reproduction number, we derive a vaccination coverage rate that is required for disease control and elimination.

Nonlinear elliptic problem involving non-local boundary conditions and variable exponent

ABSTRACT We study a nonlinear elliptic problem with non-local boundary conditions and variable exponent. We prove an existence and uniqueness result of weak solution to this problem with general maximal monotone graphs.