A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory
A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory
It is well-known that a \(C^1\) functional satisfying the (PS) condition and bounded from below, is coercive. Using the notion of the weak slope of a lower semicontinuous function, defined on a metric space, the above statement is extended to a very general version in this paper, such that almost all known results in this direction are included as special cases. A kind of ``uniform \(\Gamma\)-convergence'' and the notion of \(F\)-bounded from below are introduced in the statement.
- Bulgarian Academy of Sciences Bulgaria
- Institute of Mathematics and Informatics Bulgaria
variational principle, Nonsmooth analysis, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, Coercivity, Variational principles in infinite-dimensional spaces, nonsmooth critical point theory, Slope, Weak Slope, Variational Principle, Nonsmooth Critical Point Theory, slope, coercivity
variational principle, Nonsmooth analysis, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, Coercivity, Variational principles in infinite-dimensional spaces, nonsmooth critical point theory, Slope, Weak Slope, Variational Principle, Nonsmooth Critical Point Theory, slope, coercivity
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