Positive Ground State Solutions for a Critical Nonlocal Problem in Dimension Three

Abstract

. In this paper, we are interested in the following nonlocal problem with critical exponent where a , b are positive constants, 2 < p < 6, Ω is a smooth bounded domain in R 3 and λ > 0 is a parameter. By variational methods, we prove that problem has a positive ground state solution u b for λ > 0 sufficiently large. Moreover, we take b as a parameter and study the asymptotic behavior of u b when b ց 0.