The existence and concentration of ground-state solutions for a class of Kirchhoff type problems in R 3 ${\mathbb{R}^{3}}$ involving critical Sobolev exponents

The existence and concentration of ground-state solutions for a class of Kirchhoff type problems in R 3 ${\mathbb{R}^{3}}$ involving critical Sobolev exponents

Abstract We are concerned with ground-state solutions for the following Kirchhoff type equation with critical nonlinearity: { − ( ε 2 a + ε b ∫ R 3 | ∇ u | 2 ) Δ u + V ( x ) u = λ W ( x ) | u | p − 2 u + | u | 4 u in  R 3 , u > 0 , u ∈ H 1 ( R 3 ) , $$\textstyle\begin{cases} - ({\varepsilon^{2}}a...

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Bibliographic Details
Main Author: Chaoquan Peng
Format: Article
Language:English
Published: SpringerOpen 2017-05-01
Series:Boundary Value Problems
Subjects:
existence
concentration
Kirchhoff type equation
critical growth
Online Access:http://link.springer.com/article/10.1186/s13661-017-0793-x

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