All Questions

I have an integral operator and I wonder how I can characterize the critical point. I'll give a simplified example so maybe people can comment on and I can maybe generalize in another question. ...

Set $F:\mathbb{R}^n\rightarrow \mathbb{R}$ a $C^2$-function that is bounded from below. Set $x_n$ a minimizing sequence, i.e., $F(x_n)\to \alpha = \inf F$. I want to prove that under the assumption of ...

Index theories help characterize critical points of functionals having certain symmetries. What are the differences (regarding problems they can be applied to) between for example these ones? the ...

Let $\mathbb B^n$ be an open unit ball in $\mathbb R^n$ and let $F$ be a smooth function on it. Let $\frac{1}{2}\mathbb B^n\subset \mathbb B^n$ be an open ball or radius $\frac{1}{2}$. Let $\mathbb B^...

In various paper i found this: But i don't find this theorem of Lusternik-Schnirelmann, have you an idea where i can find this theorem, the condition? Thank you.

Condition (C). The closure of any nonempty subset S of H on which f is bounded but on which $\|\nabla f\|$is not bounded away from zero, contains a critical point of f. How to see the meaning of " $\|\...