Semilinear subelliptic problems without compactness on Lie groups (Q1884681)

The authors study an abstract version of concentration-compactness on Hilbert spaces, which applies to actions of non-compact Lie groups. By the concentration compactness method the existence of a solution of semilinear problems involving sub-Laplacians considered on the whole group or on certain non-compact subsets is proved. The case of minimizers of Sobolev inequality is also considered. The Lie group under consideration is any real connected finite-dimensional Lie group.