Morse Theory on Banach Space Its Applications to Partial Differential Equations

The author introduces a definition about the nondegeneracy of critical points of a differentiable functional defined on a Banach space. Thus the Morse theory is estabished to these functionals on a Banach space with an equivalent differentiable norm. And by use of the Morse inequalities an exension of three critical point theorem due to Krasnoselski, Castro, Lazer and the author is provided. As an application, the multiple solutions of a quasilinear elliptic boundary value problems studied.