Periodic solutions for a fractional asymptotically linear problem

Vincenzo Ambrosio; Giovanni Molica Bisci

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arXiv · 1611.01764

Periodic solutions for a fractional asymptotically linear problem

Vincenzo Ambrosio·Giovanni Molica Bisci

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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.

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Vincenzo Ambrosio, Giovanni Molica Bisci. 2016-11-06. Periodic solutions for a fractional asymptotically linear problem. https://arxiv.org/abs/1611.01764

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