Concentrated solutions for a critical nonlocal problem

Abstract

Abstract In this paper, we deal with a class of fractional critical problems. Under some suitable assumptions, we derive the existence of a positive solution concentrating at the critical point of the Robin function by using the Lyapunov–Schmidt reduction method. Comparing with previous work, we encounter some new challenges because of a nonlocal term. By making some delicate estimates for the nonlocal term we overcome the difficulty and find a bubbling solution.

Keywords

• Fractional Laplacian
• Lyapunov–Schmidt reduction method
• Critical nonlinearity