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Multiplicity results for the Ginzburg-Landau equation in presence of symmetries. (English) Zbl 0901.35029

Authors’ summary: “We prove various multiplicity results for the Ginzburg-Landau equation, when the boundary data or the manifold on which the equation is defined, verify some equivariant conditions. These results apply in particular to the functional appearing in the theory of superconductivity. Our arguments are based on the use of an \(S^1\) index (as introduced by Fadell and Rabinowitz)”.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
58J05 Elliptic equations on manifolds, general theory
35J20 Variational methods for second-order elliptic equations
82D55 Statistical mechanics of superconductors
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