In this article we study eigenvalues and minimizers of a fractional non-standard growth problem. We prove several properties on these quantities and their corresponding eigenfunctions.

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 ...

We study the following nonlocal diffusion equation in the Heisenberg group Hn,ut(z,s,t)=J∗u(z,s,t)-u(z,s,t),where ∗ denote convolution product and J satisfies appropriated hypothesis. For the Cauchy problem we obtain that ...

In this paper we study the eigenvalue problems for a nonlocal operator of order s that is analogous to the local pseudo p-Laplacian. We show that there is a sequence of eigenvalues λn→ ∞and that the first one is positive, ...

In this paper, we study the multiplicity of solutions to equations driven by a nonlocal integro-differential operator with homogeneous Dirichlet boundary conditions. In particular, using fibering maps and Nehari manifold, ...

We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove ...

We deal with boundary value problems (prescribing Dirichlet or Neumann boundary conditions) for a nonlocal nonlinear diffusion operator which is analogous to the porous medium equation. First, we prove existence, uniqueness ...

This work is concerned with implicit second order abstract differential equations with nonlocal conditions. Assuming that the involved operators satisfy sonic compactness properties, we establish the existence of local ...

This work is concerned about the existence of solutions to the nonlocal semilinear problem - N J (x - y) (u (y) - u (x)) y + h (u (x)) = f (x) x ω u = g x N ω, (-) R N J(x-y)(u(y)-u(x%)), dy+h (u(x)) = f(x),& ω u=g, x R N ...

We consider the nonlocal evolution Dirichlet problem u(t)(x, t) = f(Omega) J(x-y/g(y)) u(y, t)/g(y)(N) dy- u(x, t), x is an element of Omega, t > 0; u = 0, x is an element of R-N\Omega, t >= 0; u(x, 0) = u(0)(x), x is an ...