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Zbl 0751.58006
Brézis, Ha\" im; Nirenberg, Louis
Remarks on finding critical points. (English)
[J] Commun. Pure Appl. Math. 44, No.8-9, 939-963 (1991). ISSN 0010-3640

Let $F$ be a real $C\sp 1$ function defined on a Banach space $X$. In the first part of the paper there are presented some applications of Ekeland's Principle in obtaining critical points of functions $F$ which satisfy the Palais-Smale property. The main result is given by Theorem 1, proved in this part by using Ekeland's Principle. In the second part is presented a general deformation theorem (Theorem 3). Next a new proof of a recent theorem of Ghoussoub (Theorem 2) is given by using deformation Theorem 3. In the third part, the authors apply Theorem 2 to functions $F$ which are bounded below and satisfy the Palais-Smale property. Finally, in the Appendix, the authors give a new proof of Theorem 1 based on deformation Theorem 3.
[N.Papaghiuc (Iaşi)]

MSC 2000:: *58E05 Abstract critical point theory
58E15 Appl. of variational methods to extremal problems in sev.variables

Keywords: critical points; Palais-Smale property; Ekeland's Principle; deformation

Cited in: Zbl 1222.39005 Zbl 1240.39004 Zbl 1153.39024 Zbl 1105.49019 Zbl 1173.35473 Zbl 1096.34027 Zbl 1109.35345 Zbl 1046.34070 Zbl 1015.37016 Zbl 1014.49005 Zbl 0992.35032 Zbl 1172.58302 Zbl 0866.49013 Zbl 0863.58012 Zbl 0820.58012 Zbl 0843.58021

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