Abstract
AbstractWe consider a parametric elliptic problem governed by the spectral Neumann fractional Laplacian on a bounded domain of $$\mathbb {R}^N$$
R
N
, $$N\ge 2$$
N
≥
2
, with a general nonlinearity. This problem is related to the existence of steady states for Keller-Segel systems in which the diffusion of the chemical is nonlocal. By variational arguments we prove the existence of a weak solution as a local minimum of the corresponding energy functional and we derive some qualitative properties of this solution. Finally, we prove a regularity result for weak solutions of the problem under consideration, which is of independent interest.
Funder
Università degli Studi di Urbino Carlo Bo
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis