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Zeitschrift für Analysis und ihre Anwendungen


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Volume 20, Issue 3, 2001, pp. 553–563
DOI: 10.4171/ZAA/1030

Published online: 2001-09-30

On the Three “Essential” Critical Values Theorem

Berardino Sciunzi[1]

(1) Università della Calabria, Arcavacata di Rende, Italy

Global methods of the calculus of variations and the infinite dimensional critical point theory of Ljusternik and Schnirelmann are applied to give results on the existence of so-called critical values and essential critical values. The case of continuous, not necessarily differentiable functionals is considered and studied introducing a suitable variant of the Palais-Smale condition.

Keywords: Essential critical values, deformation lemma, Palais-Smale condition

Sciunzi Berardino: On the Three “Essential” Critical Values Theorem. Z. Anal. Anwend. 20 (2001), 553-563. doi: 10.4171/ZAA/1030