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Mountain pass theorems without Palais–Smale conditions

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Abstract

Using nonstandard analysis, we will prove two new mountain pass theorems which cannot be obtained from the well known classical mountain pass theorem of Ambrosetti–Rabinowitz.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade de Aveiro, Aveiro, Portugal

    N. Martins

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  1. N. Martins
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Correspondence to N. Martins.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 63, Optimal Control, 2009.

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Martins, N. Mountain pass theorems without Palais–Smale conditions. J Math Sci 161, 783–791 (2009). https://doi.org/10.1007/s10958-009-9599-4

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  • DOI: https://doi.org/10.1007/s10958-009-9599-4

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