Electron. J. Diff. Eqns., Vol. 2001(2001), No. 16, pp. 1-20.

A deformation theorem in the noncompact nonsmooth setting and its applications

Gianni Arioli

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.

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Gianni Arioli
Dipartimento di Scienze e T.A.
C.so Borsalino 54
15100 Alessandria Italy
e-mail: gianni@unipmn.it

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