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

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

2003-02-12

arxiv.org/abs/math/0302137v1

Mathematics

Analysis of PDEs

23 pages

Scientific paper

In order to obtain solutions to problem $$ {{array}{c} -\Delta u=\dfrac{A+h(x)} {|x|^2}u+k(x)u^{2^*-1}, x\in {\mathbb R}^N, u>0 \hbox{in}{\mathbb R}^N, {and}u\in {\mathcal D}^{1,2}({\mathbb R}^N), {array}. $$ $h$ 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.

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