On Kirchhoff type problems involving critical and singular nonlinearities

Chun-Yu Lei, et al. "On Kirchhoff type problems involving critical and singular nonlinearities." Annales Polonici Mathematici 114.3 (2015): 269-291. <http://eudml.org/doc/280989>.

@article{Chun2015,
abstract = {In this paper, we are interested in multiple positive solutions for the Kirchhoff type problem ⎧$-(a + b∫_\{Ω\} |∇u|²dx)Δu = u⁵ + λ u^\{q-1\}/|x|^\{β\}$ in Ω ⎨ ⎩ u = 0 on ∂Ω, where Ω ⊂ ℝ³ is a smooth bounded domain, 0∈Ω, 1 < q < 2, λ is a positive parameter and β satisfies some inequalities. We obtain the existence of a positive ground state solution and multiple positive solutions via the Nehari manifold method.},
author = {Chun-Yu Lei, Chang-Mu Chu, Hong-Min Suo, Chun-Lei Tang},
journal = {Annales Polonici Mathematici},
keywords = {Kirchhoff type equation; critical exponents; singular nonlinearity; concentration-compactness principle},
language = {eng},
number = {3},
pages = {269-291},
title = {On Kirchhoff type problems involving critical and singular nonlinearities},
url = {http://eudml.org/doc/280989},
volume = {114},
year = {2015},
}

TY - JOUR
AU - Chun-Yu Lei
AU - Chang-Mu Chu
AU - Hong-Min Suo
AU - Chun-Lei Tang
TI - On Kirchhoff type problems involving critical and singular nonlinearities
JO - Annales Polonici Mathematici
PY - 2015
VL - 114
IS - 3
SP - 269
EP - 291
AB - In this paper, we are interested in multiple positive solutions for the Kirchhoff type problem ⎧$-(a + b∫_{Ω} |∇u|²dx)Δu = u⁵ + λ u^{q-1}/|x|^{β}$ in Ω ⎨ ⎩ u = 0 on ∂Ω, where Ω ⊂ ℝ³ is a smooth bounded domain, 0∈Ω, 1 < q < 2, λ is a positive parameter and β satisfies some inequalities. We obtain the existence of a positive ground state solution and multiple positive solutions via the Nehari manifold method.
LA - eng
KW - Kirchhoff type equation; critical exponents; singular nonlinearity; concentration-compactness principle
UR - http://eudml.org/doc/280989
ER -