Existence of two positive solutions for a class of semilinear elliptic equations with singularity and critical exponent

Jia-Feng Liao, et al. "Existence of two positive solutions for a class of semilinear elliptic equations with singularity and critical exponent." Annales Polonici Mathematici 116.3 (2016): 273-292. <http://eudml.org/doc/280548>.

@article{Jia2016,
abstract = {We study the following singular elliptic equation with critical exponent ⎧$-Δu = Q(x)u^\{2*-1\} + λu^\{-γ\}$ in Ω, ⎨u > 0 in Ω, ⎩u = 0 on ∂Ω, where $Ω ⊂ ℝ^\{N\}$ (N≥3) is a smooth bounded domain, and λ > 0, γ ∈ (0,1) are real parameters. Under appropriate assumptions on Q, by the constrained minimizer and perturbation methods, we obtain two positive solutions for all λ > 0 small enough.},
author = {Jia-Feng Liao, Jiu Liu, Peng Zhang, Chun-Lei Tang},
journal = {Annales Polonici Mathematici},
keywords = {singular elliptic equation; critical exponent; positive solution; perturbation method},
language = {eng},
number = {3},
pages = {273-292},
title = {Existence of two positive solutions for a class of semilinear elliptic equations with singularity and critical exponent},
url = {http://eudml.org/doc/280548},
volume = {116},
year = {2016},
}

TY - JOUR
AU - Jia-Feng Liao
AU - Jiu Liu
AU - Peng Zhang
AU - Chun-Lei Tang
TI - Existence of two positive solutions for a class of semilinear elliptic equations with singularity and critical exponent
JO - Annales Polonici Mathematici
PY - 2016
VL - 116
IS - 3
SP - 273
EP - 292
AB - We study the following singular elliptic equation with critical exponent ⎧$-Δu = Q(x)u^{2*-1} + λu^{-γ}$ in Ω, ⎨u > 0 in Ω, ⎩u = 0 on ∂Ω, where $Ω ⊂ ℝ^{N}$ (N≥3) is a smooth bounded domain, and λ > 0, γ ∈ (0,1) are real parameters. Under appropriate assumptions on Q, by the constrained minimizer and perturbation methods, we obtain two positive solutions for all λ > 0 small enough.
LA - eng
KW - singular elliptic equation; critical exponent; positive solution; perturbation method
UR - http://eudml.org/doc/280548
ER -