LEAST ENERGY SOLUTIONS FOR FRACTIONAL KIRCHHOFF TYPE EQUATIONS INVOLVING CRITICAL GROWTH

被引：2

作者：

Deng, Yinbin ^{[1
,2
]}

Huang, Wentao ^{[3
]}

机构：

[1] Guangxi Univ, Sch Math & Informat, Nanning 530004, Peoples R China

[2] Cent China Normal Univ, Dept Math, Wuhan 430079, Hubei, Peoples R China

[3] East China JiaoTong Univ, Sch Sci, Nanchang 330013, Jiangxi, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2019年 / 12卷 / 07期

关键词：

Fractional Kirchhoff equation; Nehari-Pohozaev manifold; least energy solutions; critical growth; GROUND-STATE SOLUTIONS; POSITIVE SOLUTIONS; EXISTENCE; REGULARITY; BEHAVIOR;

D O I：

10.3934/dcdss.2019126

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the following fractional Kirchhoff type equation: {(a + b integral(R3)vertical bar(-Delta)(s/2)u vertical bar(2)dx) (-Delta)(s)u + V(x)u = f(u) + vertical bar u vertical bar(2s)*(-2)u, x is an element of R-3, u is an element of H-s (R-3), where a, b > 0 are constants, 2(s)* = 6/3-2s with s is an element of (0, 1) is the critical Sobolev exponent in R-3, V is a potential function on R-3. Under some more general assumptions on f and V, we prove that the given problem admits a least energy solution by using a constrained minimization on Nehari-Pohozaev manifold and monotone method.

引用

页码：1929 / 1954

页数：26

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