Some variants of one of the main results in critical point theory, namely the mountain pass lemma by A. Ambrosetti and P. H. Rabinowitz [J. Funct. Anal. 14 (1973), 349-381], are proved in this paper. In this paper we prove that if X is finite-dimensional, then the mountain may have "zero'' altitude. In the infinite-dimensional case, provided that the mountain should have nonzero "thickness''. The main tool for the proofs is a variant of a well-known lemma by Clarke. Some applications to periodic functions and periodic solutions of the forced pendulum equation are included.
A Mountain Pass Theorem
PUCCI, Patrizia;
1985
Abstract
Some variants of one of the main results in critical point theory, namely the mountain pass lemma by A. Ambrosetti and P. H. Rabinowitz [J. Funct. Anal. 14 (1973), 349-381], are proved in this paper. In this paper we prove that if X is finite-dimensional, then the mountain may have "zero'' altitude. In the infinite-dimensional case, provided that the mountain should have nonzero "thickness''. The main tool for the proofs is a variant of a well-known lemma by Clarke. Some applications to periodic functions and periodic solutions of the forced pendulum equation are included.File in questo prodotto:
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