Positive solutions for elliptic problems with critical nonlinearity and combined singularity

Chen, Jianqing, and Rocha, Eugénio M.. "Positive solutions for elliptic problems with critical nonlinearity and combined singularity." Mathematica Bohemica 135.4 (2010): 413-422. <http://eudml.org/doc/196955>.

@article{Chen2010,
abstract = {Consider a class of elliptic equation of the form \[ -\Delta u - \{\lambda \over \{|x|^2\}\}u = u^\{2^\ast -1\} + \mu u^\{-q\}\quad \mbox\{in\} \ \Omega \backslash \lbrace 0\rbrace \] with homogeneous Dirichlet boundary conditions, where $0\in \Omega \subset \mathbb \{R\}^N$($N\ge 3$), $0 < q < 1$, $0 < \lambda <(N-2)^2/4$ and $2^\ast = 2N/(N-2)$. We use variational methods to prove that for suitable $\mu $, the problem has at least two positive weak solutions.},
author = {Chen, Jianqing, Rocha, Eugénio M.},
journal = {Mathematica Bohemica},
keywords = {multiple positive solutions; singular nonlinearity; critical nonlinearity; Hardy term; multiple positive solutions; singular nonlinearity; critical nonlinearity; Hardy term},
language = {eng},
number = {4},
pages = {413-422},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Positive solutions for elliptic problems with critical nonlinearity and combined singularity},
url = {http://eudml.org/doc/196955},
volume = {135},
year = {2010},
}

TY - JOUR
AU - Chen, Jianqing
AU - Rocha, Eugénio M.
TI - Positive solutions for elliptic problems with critical nonlinearity and combined singularity
JO - Mathematica Bohemica
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 135
IS - 4
SP - 413
EP - 422
AB - Consider a class of elliptic equation of the form \[ -\Delta u - {\lambda \over {|x|^2}}u = u^{2^\ast -1} + \mu u^{-q}\quad \mbox{in} \ \Omega \backslash \lbrace 0\rbrace \] with homogeneous Dirichlet boundary conditions, where $0\in \Omega \subset \mathbb {R}^N$($N\ge 3$), $0 < q < 1$, $0 < \lambda <(N-2)^2/4$ and $2^\ast = 2N/(N-2)$. We use variational methods to prove that for suitable $\mu $, the problem has at least two positive weak solutions.
LA - eng
KW - multiple positive solutions; singular nonlinearity; critical nonlinearity; Hardy term; multiple positive solutions; singular nonlinearity; critical nonlinearity; Hardy term
UR - http://eudml.org/doc/196955
ER -