Existence of a positive ground state solution for a Kirchhoff type problem involving a critical exponent

Lan Zeng, and Chun Lei Tang. "Existence of a positive ground state solution for a Kirchhoff type problem involving a critical exponent." Annales Polonici Mathematici 117.2 (2016): 163-179. <http://eudml.org/doc/286189>.

@article{LanZeng2016,
abstract = {We consider the following Kirchhoff type problem involving a critical nonlinearity: ⎧ $-[a+b(∫_\{Ω\} |∇u|²dx)^\{m\}]Δu = f(x,u) + |u|^\{2*-2\}u$ in Ω, ⎨ ⎩ u = 0 on ∂Ω, where $Ω ⊂ ℝ^\{N\}$ (N ≥ 3) is a smooth bounded domain with smooth boundary ∂Ω, a > 0, b ≥ 0, and 0 < m < 2/(N-2). Under appropriate assumptions on f, we show the existence of a positive ground state solution via the variational method.},
author = {Lan Zeng, Chun Lei Tang},
journal = {Annales Polonici Mathematici},
keywords = {Kirchhoff type problem; critical growth; mountain pass lemma; Br'ezis-Lieb lemma; ground state solution},
language = {eng},
number = {2},
pages = {163-179},
title = {Existence of a positive ground state solution for a Kirchhoff type problem involving a critical exponent},
url = {http://eudml.org/doc/286189},
volume = {117},
year = {2016},
}

TY - JOUR
AU - Lan Zeng
AU - Chun Lei Tang
TI - Existence of a positive ground state solution for a Kirchhoff type problem involving a critical exponent
JO - Annales Polonici Mathematici
PY - 2016
VL - 117
IS - 2
SP - 163
EP - 179
AB - We consider the following Kirchhoff type problem involving a critical nonlinearity: ⎧ $-[a+b(∫_{Ω} |∇u|²dx)^{m}]Δu = f(x,u) + |u|^{2*-2}u$ in Ω, ⎨ ⎩ u = 0 on ∂Ω, where $Ω ⊂ ℝ^{N}$ (N ≥ 3) is a smooth bounded domain with smooth boundary ∂Ω, a > 0, b ≥ 0, and 0 < m < 2/(N-2). Under appropriate assumptions on f, we show the existence of a positive ground state solution via the variational method.
LA - eng
KW - Kirchhoff type problem; critical growth; mountain pass lemma; Br'ezis-Lieb lemma; ground state solution
UR - http://eudml.org/doc/286189
ER -