The Brezis–Nirenberg problem for nonlocal systems

Abstract

By means of variational methods we investigate existence, nonexistence as well as regularity of weak solutions for a system of nonlocal equations involving the fractional laplacian operator and with nonlinearity reaching the critical growth and interacting, in a suitable sense, with the spectrum of the operator.

Keywords

• fractional systems
• brezis–nirenberg problem
• nonexistence
• regularity
• 47g20
• 35j50
• 35b65