Ground state solutions for a class of fractional Kirchhoff equations with critical growth

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（5）
• 页码范围: 853-890
• 页数: 38页
• 语种: 英文

摘要

In this paper,we study the effect of lower order perturbations in the existence of positive solutions to the fractional Kirchhoff equation with critical growth (a+b∫R3|(-△)s/2u|2dx)(-△)su+V(x)u =μ|u|p-1u+|u|2*s-2u,x ∈ R3,where a,b ＞ 0 are constants,μ ＞ 0 is a parameter,s ∈(3/4,1),1 ＜ p ＜ 2*s-1 =3+2s/3-2s,and V:R3 → R is a continuous potential function.For suitable assumptions on V,we show the existence of a positive ground state solution,by using the methods of the Pohozaev-Nehari manifold,Jeanjean's monotonicity trick and the concentration-compactness principle due to Lions (1984).