Existence and multiplicity for perturbations of an equation involving Hardy inequality and critical Sobolev exponent in the whole R^N

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66507In order to obtain solutions to problem $$ {{array}{c} -Δu=\dfrac{A+h(x)} {|x|^2}u+k(x)u^{2^*-1}, x\in {\mathbb R}^N, u>0 \hbox{in}{\mathbb R}^N, {and}u\in {\mathcal D}^{1,2}({\mathbb R}^N), {array}. $$ $h$ and $k$ must be chosen taking into account not only the size of some norm but the shape. Moreover, if $h(x)\equiv 0$, to reach multiplicity of solution, some hypotheses about the local behaviour of $k$ close to the points of maximum are needed.23 pagesAnalysis of PDEs35D05, 35D10, 35J20, 35J25, 35J70, 46E30, 46E35Existence and multiplicity for perturbations of an equation involving Hardy inequality and critical Sobolev exponent in the whole R^Ntext