TY  - JOUR
ID  - Chabrowski2014
LB  - Chabrowski2014
AU  - Chabrowski, Jan
TI  - On a singular nonlinear Neumann problem
ST  - On a singular nonlinear Neumann problem
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2014
VL  - 34
IS  - 2
SP  - 271
EP  - 290
DO  - http://dx.doi.org/10.7494/OpMath.2014.34.2.271
UR  - http://dx.doi.org/10.7494/OpMath.2014.34.2.271
AB  - 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.
KW  - Neumann problem
KW  - critical Sobolev exponent
KW  - Hardy-Sobolev exponent Neumann problem
SN  - 1232-9274
ER  -