Existence and multiplicity for perturbations of an equation involving Hardy inequality and critical Sobolev exponent in the whole R^N
arXiv:math/0302137
Abstract
In order to obtain solutions to problem $$ {{array}{c} -Δu=\dfrac{A+h(x)} {|x|^2}u+k(x)u^{2^*-1}, x\in {\mathbb R}^N, u>0 \hbox{in}{\mathbb R}^N, {and}u\in {\mathcal D}^{1,2}({\mathbb R}^N), {array}. $$ and must be chosen taking into account not only the size of some norm but the shape. Moreover, if , to reach multiplicity of solution, some hypotheses about the local behaviour of close to the points of maximum are needed.
23 pages