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Multiplicity of solutions of a zero mass nonlinear equation on a Riemannian manifold. (English) Zbl 1152.58018

The paper deals with relation between the number of solutions of a nonlinear equation on a Riemannian manifold and the topology of the manifold. The machinery used is based on the Ljusternik-Schnirelmann category and Morse theory.

MSC:

58J05 Elliptic equations on manifolds, general theory
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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