Ebook: Morse Index of Solutions of Nonlinear Elliptic Equations

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.