Semilinear subelliptic problems without compactness on Lie groups

International audienceAn abstract version of concentration compactness on Hilbert spaces applies to the actions of non-compact Lie groups. Using the concentration-compactness argument we prove the existence of solutions for semilinear problems involving sub-Laplacians on the whole Lie group and on certain of their non-compact subsets, including minimizers for Sobolev inequalities. The result is stated for any real connected finite-dimensional Lie grou