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Morse Index of Solutions of Nonlinear Elliptic Equations

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Morse theory owes its name to the mathematician M. Morse who analyzed the rela- tionship between the topology of a manifold and the number and the type of critical points of a smooth function de%ned on it [180]. In some sense, it can be viewed as a beautiful and natural extension of the principle which asserts that every continuous function on a compact space has a minimum and a maximum point. The basic ideas of Morse theory can be summarized by the following two statements.

Author(s): Lucio Damascelli and Filomena Pacella
Series: De Gruyter Series in Nonlinear Analysis and Applications 30
Publisher: De Gruyter
Year: 2019

Language: English
Pages: 276

Cover......Page 1
De Gruyter Series in Nonlinear Analysis and Applications
......Page 3
Morse Index of Solutions of Nonlinear Elliptic Equations
......Page 5
© 2019......Page 6
Preface......Page 7
Contents
......Page 11
Notation
......Page 15
1 Preliminaries......Page 19
2 Introduction to Morse theory......Page 77
3 Morse theory for semilinear elliptic equations......Page 101
4 Morse index of radial solutions of Lane–Emden
problems......Page 139
5 Bifurcation from radial solutions......Page 173
6 Morse index and symmetry for semilinear elliptic
equations in bounded domains......Page 195
7 Morse index and symmetry for elliptic systems in
bounded domains......Page 231
8 Some results in unbounded domains......Page 253
Bibliography......Page 263
Index......Page 273