Two weak solutions for perturbed non-local fractional equations

Abstract

In the present paper, we consider problems modeled by the following non-local fractional equation:where is fixed, is the fractional Laplace operator, are real parameters, is an open bounded subset of () with Lipschitz boundary , and are two suitable Carathéodory functions. By using variational methods, we prove the existence of at least two weak solutions for such problems for certain values of the parameters.

Keywords:

• variational methods
• integrodifferential operators
• fractional Laplacian

AMS Subject Classifications:

• Primary: 49J35
• 35A15
• 35S15
• Secondary: 47G20
• 45G05

Additional information

Funding

The first author was supported by the project titled: Variational, topological and algebraic methods for non-linear elliptic problems when he visited University of Reggio Calabria and Medalics Research Centre in Reggio Calabria. The first author was also supported by the Natural Science Foundation of Heilongjiang Province of China under [grant number A201306] and the Doctoral Research Foundation of Heilongjiang Institute of Technology under [grant number 2013BJ15].