Author: A. Lehtonen

0000000001300178

AUTHOR

A. Lehtonen

On the construction of Ljusternik-Schnirelmann critical values in banach spaces

w h e r e f a n d g are functionals on a Banach space X, are considered in many papers. The existence theorems are based on the existence of a critical vector with respect to the manifold M,={xEX: f(x)=r}. Morse theory can often be used to obtain precise information about the behaviour of the functional close to the critical level. However, this would limit the study to Hilbert spaces and functions with nondegenerate critical points. These assumptions are not always satisfied in applications and are not rleeded when applying the Ljusternik--Schnirelmann theory. Therefore, Ljusternik--Schnirelmann theory has been widely used to study various nonlinear eigenvalue problems. Very general result…

0000000001300178

AUTHOR

A. Lehtonen

On the construction of Ljusternik-Schnirelmann critical values in banach spaces

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