Nabla theorems and multiple solutions for some noncooperative elliptic systems

Antonio Marino, Claudio Saccon

DOI: http://dx.doi.org/10.12775/TMNA.2001.014

Abstract


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 suitable
sets. We derive some multiplicity theorems for a certain class of
strongly indefinite functionals and we apply these results for finding
multiple solutions of an elliptic system of reaction-diffusion type.

Keywords


Nabla theorems; strongly indefinite functionals; limit relative category; reaction-diffusion elliptic systems

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