Compactness of Palais-Smale sequences with controlled Morse Index for a
Liouville type functional
Compactness of Palais-Smale sequences with controlled Morse Index for a
Liouville type functional
We prove that Palais-Smale sequences for Liouville type functionals on closed surfaces are precompact whenever they satisfy a bound on their Morse index. As a byproduct, we obtain a new proof of existence of solutions for Liouville type mean-field equations in a supercritical regime. Moreover, we also discuss an extension …