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Two variational methods on manifolds with boundary. (English) Zbl 0819.58003
The reviewing article deals with a twofold extension of the classical deformation lemma in the calculus of variations to the setting of infinite-dimensional manifolds with boundary. Such extension of the deformation lemmas is motivated by an attempt to overcome difficulties arising when using the classical Lyusternik-Schnirelman theory in the applications. Concerning the prerequisites and the basic results the author refers to the fundamental works of R. S. Palais [ibid. 2, 299-340 (1963; Zbl 0122.107) and ibid. 5, 115-132 (1966; Zbl 0143.352)].

MSC:
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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