Książka - szczegóły

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coefficients Q and h are at least continuous. Moreover Q is positive on Ω̅ and λ > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coefficients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by -Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.