×

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

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.

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

Citations:

Zbl 0872.58018
PDF BibTeX XML Cite
Full Text: DOI