Compactness and the Palais–Smale property for critical Kirchhoff equations in closed manifolds
Emmanuel Hebey · Pacific Journal of Mathematics · 2016
We prove the Palais-Smale property and the compactness of solutions for critical Kirchhoff equations using solely energy arguments in the situation where no sign assumption is made on the solutions.We then prove the existence of a mountain-pass solution to the equation, discuss its ground-states structure, and, in extreme cases, prove uniqueness of this solution.