International Journal of Functional Analysis, Operator Theory and Applications
Volume 2, Issue 1, Pages 57 - 66
(June 2010)
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A CRITICAL POINT THEOREM FOR NONCONTINUOUS FUNCTIONALS
Rebecca Walo Omana and Issa Ramadhani
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Abstract:
We present an abstract critical point theorem dropping any smoothness or continuity assumptions on the functional. The main tools are quantitative equivariant deformation properties. As a by-product, we prove an existence result of infinitely many critical values for an invariant and noncontinuous functional on a complete metric space. This result generalizes the nonsmooth and noncontinuous cases, the so-called “Fountain theorem”. |
| Keywords and phrases: nonsmooth functional, equivariance, critical value, Fountain theorem. |
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