Bifurcation and multiplicity of positive solutions for nonhomogeneous fractional Schr(o)dinger equations with critical growth

• 作者: Wenming Zou Xiaoming He
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2020,（8）
• 所属期刊栏目: Articles
• 页码范围: 1571-1612
• 页数: 42页
• 语种: 英文

摘要

In this paper we study the nonhomogeneous semilinear fractional Schr(o)dinger equation with critical growth{(-△)su+u=u2*s-1 +λ(f(x,u)+h(x)),x∈RN,u ∈ Hs(RN),u(x) ＞ 0,x ∈ RN,where s ∈ (0,1),N ＞ 4s,and λ ＞ 0 is a parameter,2*s =2N/N-2s is the fractional critical Sobolev exponent,f and h are some given functions.We show that there exists 0 ＜ λ* ＜ +∞ such that the problem has exactly two positive solutions if λ ∈ (0,λ*),no positive solutions for λ ＞ λ*,a unique solution (λ*,uλ*) if λ =λ*,which shows that (λ*,uλ*) is a turning point in Hs(RN) for the problem.Our proofs are based on the variational methods and the principle of concentration-compactness.

作者信息

序号	姓名	单位	发文数	被引次数	H指数	G指数
1	Xiaoming He		1	0	0.0	0.0
2	Wenming Zou		1	0	0.0	0.0