Homology of saddle point reduction and applications to resonant elliptic systems. (English) Zbl 1262.58011

Li, Chong; Liu, Shibo

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 81, 236-246 (2013).

Summary: In the setting of saddle point reduction, we prove that the critical groups of the original functional and the reduced functional are isomorphic. As application, we obtain two nontrivial solutions for elliptic gradient systems which may be resonant both at the origin and at infinity. The difficulty that the variational functional does not satisfy the Palais-Smale condition is overcame by taking advantage of saddle point reduction. Our abstract results on critical groups are crucial.

MSC:

58E05	Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
35J60	Nonlinear elliptic equations

Keywords:

critical groups; saddle point reduction; Künneth formula; resonant elliptic systems