Morse Theory

Dumitru Motreanu, Viorica Venera Motreanu and Nikolaos Papageorgiou
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Dumitru Motreanu: University of Perpignan, Department of Mathematics
Viorica Venera Motreanu: Ben-Gurion University of the Negev, Department of Mathematics
Nikolaos Papageorgiou: National Technical University, Department of Mathematics

Chapter Chapter 6 in Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems, 2014, pp 141-179 from Springer

Abstract: Abstract This chapter represents a self-contained presentation of basic results and techniques of Morse theory that are useful for studying the multiplicity of solutions of nonlinear elliptic boundary value problems with a variational structure. The first section of the chapter contains the needed preliminaries of algebraic topology. The second section focuses on the Morse lemma and the splitting and shifting theorems. The third section is devoted to the Morse relations, including the Poincaré–Hopf formula, which involve the critical groups and critical groups at infinity. The fourth section sets forth efficient results for the computation of critical groups that are powerful tools in the study of multiple solutions. Here an original approach is developed, and improvements of known results are shown. Notes on related literature and comments are provided in a remarks section.

Keywords: Morse Relations; Morse Lemma; Radical Critique; Mountain Pass Type; Mawhin (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-9323-5_6

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DOI: 10.1007/978-1-4614-9323-5_6

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