6 research outputs found
Attainability of the fractional Hardy constant with nonlocal mixed boundary conditions. Applications
The first goal of this paper is to study necessary and sufficient conditions
to obtain the attainability of the \textit{fractional Hardy inequality }
where is a
bounded domain of , , a nonempty open set and The second aim of the paper
is to study the \textit{mixed Dirichlet-Neumann boundary problem} associated to
the minimization problem and related properties; precisely, to study semilinear
elliptic problem for the \textit{fractional laplacian}, that is, with and
open sets in such that and
, ,
and , . We emphasize that
the nonlinear term can be critical.
The operators , fractional laplacian, and ,
nonlocal Neumann condition, are defined below in (1.5) and (1.6) respectively
A nonlocal concave-convex problem with nonlocal mixed boundary data
The aim of this paper is to study a nonlocal equation with mixed Neumann and Dirichlet external conditions. We prove existence, nonexistence and multiplicity of positive energy solutions and analyze the interaction between the concave-convex nonlinearity and the Dirichlet-Neumann data
Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods
We consider positive solutions of a fractional Lane-Emden type problem in a
bounded domain with Dirichlet conditions. We show that uniqueness and
nondegeneracy hold for the asymptotically linear problem in general domains.
Furthermore, we also prove that all the known uniqueness and nondegeneracy
results in the local case extend to the nonlocal regime when the fractional
parameter s is sufficiently close to 1.Comment: 22 page
A nonlocal concave-convex problem with nonlocal mixed boundary data
The aim of this paper is to study a nonlocal equation with mixed Neumann and Dirichlet external conditions. We prove existence, nonexistence and multiplicity of positive energy solutions and analyze the interaction between the concave-convex nonlinearity and the Dirichlet-Neumann data
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A nonlocal concave-convex problem with nonlocal mixed boundary data
The aim of this paper is to study a nonlocal equation with mixed Neumann and Dirichlet external conditions. We prove existence, nonexistence and multiplicity of positive energy solutions and analyze the interaction between the concave-convex nonlinearity and the Dirichlet-Neumann data
A nonlocal concave-convex problem with nonlocal mixed boundary data
The aim of this paper is to study a nonlocal equation with mixed Neumann and Dirichlet external conditions. We prove existence, nonexistence and multiplicity of positive energy solutions and analyze the interaction between the concave-convex nonlinearity and the Dirichlet-Neumann data