Applications of local linking to critical point theory. (English) Zbl 0820.58012

Li, Shujie; Willem, Michel

J. Math. Anal. Appl. 189, No. 1, 6-32 (1995).

The notion of local linking is extended to case where the Banach space is decomposed into a direct sum of two infinite dimensional linear subspaces [see H. Brezis and L. Nirenberg, Commun. Pure Appl. Math. 44, No. 8/9, 939-963 (1991; Zbl 0751.58006)]. Some existence theorems for nontrivial critical points of functionals with a local linking at 0 are extended. Applications to elliptic BVP and to Hamiltonian systems are given.

Reviewer: Chang Kungching (Beijing)

MSC:

58E05

Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces

Keywords:

elliptic boundary value problem; Hamiltonian system; critical points; local linking

Citations:

Zbl 0751.58006