Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 16, pp. 1-20.
Title: A deformation theorem in the noncompact nonsmooth setting
and its applications
Author: Gianni Arioli (Dipartimento di Scienze e T.A., Alessandria Italy)
Abstract:
We build a deformation for a continuous functional defined on a Banach space
and invariant with respect to an isometric action of a noncompact group.
Under these assumptions the Palais-Smale condition does not hold. When the
functional is also invariant with respect to the action of a compact Lie
group, we prove 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, we prove the existence of infinitely
many solutions.
Submitted September 15, 2000. Published February 23, 2001.
Math Subject Classifications: 35D05, 35J20, 35J60.
Key Words: Quasilinear elliptic differential systems; Equivariant category;
Nonsmooth critical point theory.