Bifurcation results for the critical Choquard problem involving fractional p-Laplacian operator

作者：Wang, Yuling; Yang, Yang^*

来源：Boundary Value Problems, 2018, 2018(1): 132.

DOI：10.1186/s13661-018-1050-7

• Fractional p-Laplacian
• Choquard equation
• Critical exponent
• Z(2)-cohomological index
• Pseudo-index

By using an abstract critical point theorem based on a pseudo-index related to the cohomological index, we prove the bifurcation results for the critical Choquard problems involving fractional p-Laplacian operator: @@@ (-Delta)(p)(s)u = lambda vertical bar u vertical bar(p-2)u + (integral(Omega )vertical bar u vertical bar(p)* mu,s/vertical bar X-Y vertical bar mu dy)vertical bar u vertical bar p(*)mu,s-2 u in Omega, u = 0 in R-N Omega @@@ where Omega is a bounded domain in R-N with Lipschitz boundary, lambda is a real parameter, p is an element of (1, infinity), s is an element of (0,1), N > sp, and p(mu,s)* = (N-mu/2)p/N-sp is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality. These extend results in the literature for the fractional Choquard problems, and they are still new for a p-Laplacian case.

• 单位
  江南大学