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Asymptotic behavior for nonlocal diffusion equations
We study the asymptotic behavior for nonlocal diffusion models of the form ut=J∗u−u in the whole RN or in a bounded smooth domain with Dirichlet or Neumann boundary conditions. In RN we obtain thatExpand
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Nonlocal Diffusion Problems
Nonlocal diffusion problems arise in a wide variety of applications, including biology, image processing, particle systems, coagulation models, and mathematical finance. These types of problems areExpand
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An asymptotic mean value characterization for p-harmonic functions
We characterize p-harmonic functions in terms of an asymptotic mean value property. A p-harmonic function u is a viscosity solution to Δ p u = div(|∇u| p-2 ∇u) = 0 with 1 < p ≤ ∞ in a domain Ω if andExpand
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On the definition and properties of p-harmonious functions
We consider functions that satisfy the identity ue(x) = α 2 { sup Be(x) ue + inf Be(x) ue } + β ∫
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A convex-concave problem with a nonlinear boundary condition
In this paper we study the existence of nontrivial solutions of the problem {-Δu+u = u p-2u in Ω, {∂u/∂v = λ u q-2u on ∂Ω, with 1<q<2(N-1)/(N-2) and 1<p≤2N/(N-2). In the concave-convex case, i.e.,Expand
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On the principal eigenvalue of some nonlocal diffusion problems
Abstract In this paper we analyze some properties of the principal eigenvalue λ 1 ( Ω ) of the nonlocal Dirichlet problem ( J ∗ u ) ( x ) − u ( x ) = − λ u ( x ) in Ω with u ( x ) = 0 in R N ∖ Ω .Expand
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Boundary blow-up solutions to elliptic systems of competitive type
Abstract We consider the elliptic system Δ u = u p v q , Δ v = u r v s in Ω , where p , s > 1 , q , r > 0 , and Ω ⊂ R N is a smooth bounded domain, subject to different types of Dirichlet boundaryExpand
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Fractional Sobolev spaces with variable exponents and fractional p(x)-Laplacians
In this article we extend the Sobolev spaces with variable exponents to include the fractional case, and we prove a compact embedding theorem of these spaces into variable exponent Lebesgue spaces.Expand
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A nonlocal convection–diffusion equation
In this paper we study a nonlocal equation that takes into account convective and diffusive effects, ut=J∗u−u+G∗(f(u))−f(u) in Rd, with J radially symmetric and G not necessarily symmetric. First, weExpand
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On the Fučik spectrum and a resonance problem for the p-Laplacian with a nonlinear boundary condition
In this paper we prove that there exists a first curve of the Fucik spectrum of the problem Δpu=|u|p-2u in Ω with a nonlinear boundary condition given by |∇u|p-2∂u/∂ν=α(u+)p-1-β(u-)p-1 on theExpand
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