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

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.

MSC:

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

Citations:

Zbl 0751.58006
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