Min-max solutions for super sinh-Gordon equations on compact surfaces. (English) Zbl 1464.58006
In this paper the authors study a super sinh-Gordon system on compact surfaces. In the main result they get the existence of a non-trivial solution of min-max type for it using variational methods. Precisely, the proof is based on a Linking argument jointly with a suitably defined Nehari manifold and a careful study of the Palais-Smale condition, which is based on spectral decomposition and suitable test functions. Finally, the authors give a multiplicity result by exploiting the \(Z_2\)-symmetry of the problem.
Reviewer: Raffaella Servadei (Arcavata di Rende)
MSC:
| 58J05 | Elliptic equations on manifolds, general theory |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 58E05 | Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces |
| 81Q60 | Supersymmetry and quantum mechanics |
Keywords:
super sinh-Gordon equations; variational methods; min-max methods; existence and multiplicity resultsReferences:
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