On the Neumann problem for an elliptic system of equations involving the critical Sobolev exponent
Volume 90 / 2001
Colloquium Mathematicum 90 (2001), 19-35
MSC: 35J50, 35J55, 35B33.
DOI: 10.4064/cm90-1-2
Abstract
We consider the Neumann problem for an elliptic system of two equations involving the critical Sobolev nonlinearity. Our main objective is to study the effect of the coefficient of the critical Sobolev nonlinearity on the existence and nonexistence of least energy solutions. As a by-product we obtain a new weighted Sobolev inequality.
