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Morse‐type information on palais‐smale sequences obtained by min‐max principles
Author(s) -
Fang G.,
Ghoussoub N.
Publication year - 1994
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160471204
Subject(s) - mathematics , morse code , compact space , morse theory , context (archaeology) , type (biology) , a priori and a posteriori , convergence (economics) , critical point (mathematics) , dual (grammatical number) , point (geometry) , pure mathematics , mathematical analysis , geometry , computer science , art , telecommunications , paleontology , ecology , philosophy , literature , epistemology , economics , biology , economic growth
In the context of the min‐max approach to critical point theory, but without the usual compactness assumptions à la Palais‐Smale and the nondegeneracy conditions à la Fredholm, we construct almost critical points with two‐sided estimates on their approximate Morse indices which are arbitrarily close to certain—a priori given— dual sets. This additional topological and analytical information about almost critical sequences can sometimes be crucial in the proof of their convergence and therefore in solving the corresponding variational problem. © 1994 John Wiley & Sons, Inc.