Changing-sign solutions for the CR-Yamabe equation

Abstract

In this paper we prove that the CR-Yamabe equation on the Heisenberg group has infinitely many changing-sign solutions. By means of the Cayley transform we will set the problem on the sphere $S^{2n+1}$; since the functional $I$ associated with the equation does not satisfy the Palais-Smale compactness condition, we will find a suitable closed subspace $X$ on which we can apply the minmax argument for $I_{|X}$. We generalize the result to any compact contact manifold of $K$-contact type.