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.