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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:
58J05Elliptic equations on manifolds, general theory
58E05Abstract critical point theory
References:
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[8]Berestycki, H.; Lions, P. -L.: Existence d’états multiples dans des équations de champs scalaires non linéaires dans le cas de masse nulle, C. R. Acad. sci. Paris sér. I math. 297, No. 4, 267-270 (1983) · Zbl 0542.35072
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[11]De Figueiredo, D. G.: Lectures on the Ekeland variational principle with applications and detours, Tata inst. Fund. res. Lect. math. Phys. 81 (1989)
[12]Hebey, E.: Nonlinear analysis on manifolds: Sobolev spaces and inequalities, Courant lect. Notes math. 5 (1999)
[13]Ljusternik, L.; Schnirelmann, L.: Méthodes topologiques dans LES problèmes variationelles, Actualites sci. Industr. 188 (1934) · Zbl 60.1228.04
[14]Milnor, J.: Morse theory, Ann. of math. Stud. 51 (1963)
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