A deformation theorem in the noncompact nonsmooth setting and its applications (Q2703371)

The author builds a deformation for a continuous functional defined on a Banach space and invariant with respect to an isometric action of a non-compact group. Under these assumptions the Palais-Smale conditions does not hold. When the functional is also invariant with respect to the action of a compact Lie group, the author proves that the deformation can be chosen to be equivariant with respect to the same action. In the second part of the paper a system of periodic quasilinear partial differential equations invariant under the action of some compact Lie group is considered. Using the deformation technique developed in the first part, the author proves the existence of infinitely many solutions.