Arkiv för Matematik

Volume 58 (2020)

Number 1

A multiplicity result for a non-local parametric problem with periodic boundary conditions

Pages: 1 – 18



Vincenzo Ambrosio (Dipartimento di Ingegneria Industriale e Scienze Matematiche, Università Politecnica delle Marche, Ancona, Italy)

Rossella Bartolo (Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Italy)

Giovanni Molica Bisci (Dipartimento di Scienze Pure e Applicate (DiSPeA), Università degli Studi di Urbino Carlo Bo, Urbino, Italy)


We look for bounded periodic solutions for a parametric fractional problem involving a continuous nonlinearity with subcritical growth. By using a variant of Caffarelli and Silvestre extension method adapted to the periodic case and variational tools we prove the existence of at least three bounded periodic solutions when the parameter varies in an appropriate range.


fractional operators, periodic solutions, variational methods, multiple solutions

2010 Mathematics Subject Classification

Primary 49J35. Secondary 35A15, 35S15, 47G20.

Received 13 November 2018

Received revised 10 April 2019

Accepted 17 May 2019

Published 21 July 2022