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We study some variational principles which imply the existence of multiple critical points for a functional $f$, using the properties of both $f$ and $\nabla f$ on some suitablesets. We derive some multiplicity theorems for a certain class ofstrongly indefinite functionals and we apply these results for findingmultiple solutions of an elliptic system of reaction-diffusion type.

Nabla theorems and multiple solutions for some noncooperative elliptic systems