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Linking–preserving perturbations of symmetric functionals. (English) Zbl 1247.58012

Summary: We consider paths of functionals starting with one which is invariant under the action of an arbitrary group of symmetries. We give conditions for the existence of an unbounded sequence of critical values of the non-symmetric functional at the end of the path in terms of the growth of the critical values of the symmetric one. We apply this to obtain a multiplicity result for a system of elliptic equations whose symmetries are perturbed by a linear term and a non-homogeneous boundary condition.

MSC:

58E40 Variational aspects of group actions in infinite-dimensional spaces
35A30 Geometric theory, characteristics, transformations in context of PDEs
35B38 Critical points of functionals in context of PDEs (e.g., energy functionals)
35J20 Variational methods for second-order elliptic equations
35J60 Nonlinear elliptic equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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