Damascelli, Lucio / Pacella, Filomena
Morse Index of Solutions of Nonlinear Elliptic Equations
- An in-depth monograph on Morse index techniques for nonlinear elliptic equations
- Discusses the connections of the Morse index with the maximum principle
- Studies several qualitative properties of solutions like well-posedness, symmetry, etc.
Aims and Scope
This monograph presents in a unified manner the use of the Morse index, and especially its connections to the maximum principle, in the study of nonlinear elliptic equations. The knowledge or a bound on the Morse index of a solution is a very important qualitative information which can be used in several ways for different problems, in order to derive uniqueness, existence or nonexistence, symmetry, and other properties of solutions.