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. As an application we ...

We prove the existence of an unbounded branch of solutions to the nonlinear non-local equation (Equation presented) bifurcating from the first eigenvalue. Here (-Δ)s p denotes the fractional p-Laplacian and Ω ⊂ ℝ1 is a ...

We study the symmetry breaking phenomenon for an elliptic equation involving the fractional Laplacian in a large ball. Our main tool is an extension of the Strauss radial lemma involving the fractional Laplacian, which ...

Our propose here is to provide a Hopf lemma and a strong minimum principle for weak supersolutions of (−Δp)su=c(x)|u|p−2u in Ω where Ω is an open set of RN, s∈(0,1), p∈(1,+∞), c∈C(Ω‾) and (−Δp)s is the fractional p-Laplacian.

In this paper, we establish a multiplicity result of nontrivial weak solutions for the problem (- Δ) αu+ u= h(u) in Ω λ, u= 0 on ∂Ω λ, where Ω λ= λΩ , Ω is a smooth and bounded domain in RN, N> 2 α, λ is a positive parameter, ...

In this work we study the homogenization for eigenvalues of the fractional p-Laplace operator in a bounded domain both with Dirichlet and Neumann conditions. We obtain the convergence of eigenvalues and the explicit order ...

We examine a fractional version of the discrete nonlinear Schrodinger (dnls) equation, where the usual discrete laplacian is replaced by a fractional discrete laplacian. This leads to the replacement of the usual ...

The aim of this work is to study certain type of operators that have adquired a renewed relevance in the last decade. This wide class of operators, genericaly called nonlocal operators, appears naturally in many applications ...

In this paper we extend two nowadays classical results to a nonlinear Dirichlet problem to equations involving the fractional p-Laplacian. The first result is an existence in a non-resonant range more specific between the ...

In this work, we present results of existence, non-existence and multiplicity of positive solutions to elliptic problems involving the fractional p-Laplacian operator and the fractional Laplacian in the critical case, ...