82 research outputs found
1/2-Laplacian problems with exponential nonlinearity
By exploiting a suitable Trudinger-Moser inequality for fractional Sobolev
spaces, we obtain existence and multiplicity of solutions for a class of
one-dimensional nonlocal equations with fractional diffusion and nonlinearity
at exponential growth.Comment: 10 page
Weyl-type laws for fractional p-eigenvalue problems
We prove an asymptotic estimate for the growth of variational eigenvalues of
fractional p-Laplacian eigenvalue problems on a smooth bounded domain.Comment: 10 page
Existence and multiplicity results for resonant fractional boundary value problems
We study a Dirichlet-type boundary value problem for a pseudo-differential
equation driven by the fractional Laplacian, with a non-linear reaction term
which is resonant at infinity between two non-principal eigenvalues: for such
equation we prove existence of a non-trivial solution. Under further
assumptions on the behavior of the reaction at zero, we detect at least three
non-trivial solutions (one positive, one negative, and one of undetermined
sign). All results are based on the properties of weighted fractional
eigenvalues, and on Morse theory
A note on global regularity for the weak solutions of fractional p-Laplacian equations
We consider a boundary value problem driven by the fractional p-Laplacian
operator with a bounded reaction term. By means of barrier arguments, we prove
H\"older regularity up to the boundary for the weak solutions, both in the
singular (12) case.Comment: 7 pages, Conferenza tenuta al XXV Convegno Nazionale di Calcolo delle
Variazioni, Levico 2--6 febbraio 201
Ground states for scalar field equations with anisotropic nonlocal nonlinearities
We consider a class of scalar field equations with anisotropic nonlocal
nonlinearities. We obtain a suitable extension of the well-known compactness
lemma of Benci and Cerami to this variable exponent setting, and use it to
prove that the Palais-Smale condition holds at all level below a certain
threshold. We deduce the existence of a ground state when the variable exponent
slowly approaches the limit at infinity from below.Comment: 10 page
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