On the critical Neumann problem with weight in exterior domains Original Research Article

In this paper we investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent in exterior domains. It is assumed that the coefficient Q is a positive and smooth function on Ωc and λ>0 is a parameter. We examine the common effect of the mean curvature of the boundary View the MathML source and the shape of the graph of the coefficient Q on the existence of least energy solutions.