On nonlocal Dirichlet problems with oscillating term

On homogenization problems for fully nonlinear equations with oscillating Dirichlet boundary conditions

We study two types of asymptotic problems whose common feature and difficultyis to exhibit oscillating Dirichlet boundary conditions : the main contribution of this article is to show how to recover the Dirichlet boundary condition for the limiting equation. These two types of problems are (i) periodic homogenization problems for fully nonlinear, second-order elliptic partial differential equat...

Nonlocal Diffusion Problems That Approximate the Heat Equation with Dirichlet Boundary Conditions

We present a model for nonlocal diffusion with Dirichlet boundary conditions in a bounded smooth domain. We prove that solutions of properly re-scaled non local problems approximate uniformly the solution of the corresponding Dirichlet problem for the classical heat equation.

Dirichlet Problems with Asymmetric Nonlinearities

On a Class of Nonlocal Elliptic Problems with Critical Growth

This paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the Kirchhoff type − [ M (∫ Ω |∇u|2 dx )] Δu = λ f (x,u)+u in Ω,u(x) > 0 in Ω and u = 0 on ∂Ω, where Ω ⊂ RN , for N=1,2 and 3, is a bounded smooth domain, M and f are continuous functions and λ is a positive parameter. Our approach is based on the variational method.

Nonlocal Problems with Neumann Boundary Conditions

We introduce a new Neumann problem for the fractional Laplacian arising from a simple probabilistic consideration, and we discuss the basic properties of this model. We can consider both elliptic and parabolic equations in any domain. In addition, we formulate problems with nonhomogeneous Neumann conditions, and also with mixed Dirichlet and Neumann conditions, all of them having a clear probab...