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.
@book{bwmeta1.element.bwnjournal-rm-doi-10_4064-dm417-0-1, author = {J. Chabrowski and E. Tonkes}, title = {On the nonlinear Neumann problem with critical and supercritical nonlinearities}, series = {GDML\_Books}, year = {2003}, zbl = {1273.35125}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm417-0-1} }
J. Chabrowski; E. Tonkes. On the nonlinear Neumann problem with critical and supercritical nonlinearities. GDML_Books (2003), http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm417-0-1/