Decomposition lemmes applied to Hardy-Sobolev type inequalities

Decomposition (or concentration-compactness) lemmas have already shown their efficience in order to show existence of minimizers or ground state solutions. The aim of this paper is to apply new version of these lemmas to minimisation problems involving Hardy-Sobolev type inequalities on a specific class of unbounded domains. More precisely, we shall find ground state solution for the following quotient, where value of real numbers epsilon, b, q and a are given. [GRAPHICS] We shall end this paper by establishing a decomposition lemma for cylindrical domains. More precisely, we shall find a minimizer for the following quantity: [GRAPHICS]