Periodic solutions for a fractional asymptotically linear problem
Analysis of PDEs
2018-09-06 v2
Abstract
We study the existence and multiplicity of periodic weak solutions for a non-local equation involving an odd subcritical nonlinearity which is asymptotically linear at infinity. We investigate such problem by applying the the pseudo-index theory developed by Bartolo, Benci and Fortunato \cite{bbf} after transforming the problem to a degenerate elliptic problem in a half-cylinder with a Neumann boundary condition, via a Caffarelli-Silvestre type extension in periodic setting. The periodic nonlocal case, considered here, presents, respect to the cases studied in literature, some new additional difficulties and a careful analysis of the fractional spaces involved is necessary.
Cite
@article{arxiv.1611.01764,
title = {Periodic solutions for a fractional asymptotically linear problem},
author = {Vincenzo Ambrosio and Giovanni Molica Bisci},
journal= {arXiv preprint arXiv:1611.01764},
year = {2018}
}