ASYMMETRIC CRITICAL FRACTIONAL p-LAPLACIAN PROBLEMS

作者：Huang, Li; Yang, Yang^*

来源：Electronic Journal of Differential Equations, 2017, 103.

• Fractional p-Laplacian
• critical nonlinearity
• asymmetric nonlinearity
• linking
• Z(2)-cohomological index

We consider the asymmetric critical fractional p-Laplacian problem @@@ (-Delta)(p)(s)u = lambda vertical bar u vertical bar(p-2)u + u(+)(s)(p)*-1 , in Omega; @@@ u = 0, in R-N \ Omega; @@@ where lambda > 0 is a constant, p(s)* = Np/(N - sp) is the fractional critical Sobolev exponent, and u(+) (x) = max{u(x), 0}. This extends a result in the literature for the local case s = 1. We prove the theorem based on the concentration compactness principle of the fractional p-Laplacian and a linking theorem based on the Z(2)-cohomological index.

• 单位
  江南大学