Two variational methods on manifolds with boundary (Q1344443)

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 \textit{R. S. Palais} [ibid. 2, 299-340 (1963; Zbl 0122.107) and ibid. 5, 115-132 (1966; Zbl 0143.352)].