Asymptotically linear fractional Schrödinger equations

Abstract

By exploiting a variational technique based upon projecting over the Pohožaev manifold, we prove existence of positive solutions for a class of nonlinear fractional Schrödinger equations having a nonhomogenous nonautonomous asymptotically linear nonlinearity.

Keywords:

• fractional Laplacian
• ground states
• Pohožaev identity
• critical point theory

AMS Subject Classifications:

• 34A08
• 35Q40
• 58E05

Acknowledgements

We thank the anonymous reviewers for their careful reading of our manuscript and their insightful comments and suggestions.

Additional information

Funding

The first author is supported by UNIOESTE/CCET and partially supported by CAPES/AEX 3410/14-5. The second author is partially supported by CNPq/ PQ 306388/2011-1. The third author is partially supported by 2009 MIUR project: “Variational and Topological Methods in the Study of Nonlinear Phenomena”.