A new Morse theory and strong resonance problems. (English) Zbl 1053.58005

Li, Shujie

Topol. Methods Nonlinear Anal. 21, No. 1, 81-100 (2003).

In this interesting paper the author presents a Morse type theory for functions \(f\) which do not satisfy the (PS) condition at some isolated values. He also considers some multiplicity results for strong resonance problems in connection to multiple resonant energy levels.
I want to mention that such a theory was first introduced by T. Bartsch and the author [Nonlinear Anal., Theory Methods Appl. 28, No. 3, 419–441 (1997; Zbl 0872.58018)] for the local behavior of functions \(f\) near infinity.

Reviewer: D. Andrica (Cluj-Napoca)

MSC:

58E05	Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
35J65	Nonlinear boundary value problems for linear elliptic equations

Keywords:

Morse theory; strong resonance problems; elliptic boundary value problems

Citations:

Zbl 0872.58018