@Article{Chabrowski2014,
author = "Chabrowski, Jan",
title = "On a singular nonlinear Neumann problem",
journal = "Opuscula Math.",
year = "2014",
volume = "34",
number = "2",
pages = "271--290",
doi = "http://dx.doi.org/10.7494/OpMath.2014.34.2.271",
url = "http://dx.doi.org/10.7494/OpMath.2014.34.2.271",
abstract = "We investigate the solvability of the Neumann problem involving two critical exponents: Sobolev and Hardy-Sobolev. We establish the existence of a solution in three cases: \(\text{(i)}\;\ 2\lt p+1\lt 2^*(s),\) \(\text{(ii)}\;\ p+1=2^*(s)\) and \(\text{(iii)}\;\ 2^*(s)\lt p+1 \leq 2^*,\) where \(2^*(s)=\frac{2(N-s)}{N-2},\) \(0\lt s\lt 2,\) and \(2^*=\frac{2N}{N-2}\) denote the critical Hardy-Sobolev exponent and the critical Sobolev exponent, respectively.",
keywords = "Neumann problem, critical Sobolev exponent, Hardy-Sobolev exponent Neumann problem",
issn = "1232-9274"
}