Arkiv för Matematik
Volume 58 (2020)
A multiplicity result for a non-local parametric problem with periodic boundary conditions
Pages: 1 – 18
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