Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Global Diffeomorphism Theorem for Fr\'{e}chet spaces   We give sufficient conditions for a $ C^1_c $-local diffeomorphism between
Fr\'{e}chet spaces to be a global one. We extend the Clarke's theory of
generalized gradients to the more general setting of Fr\'{e}chet spaces. As a
consequence, we define the Chang Palais-Smale condition for Lipschitz functions
and show that a function which is bounded below and satisfies the Chang
Palais-Smale condition at all levels is coercive. We prove a version of the
mountain pass theorem for Lipschitz maps in the Fr\'{e}chet setting and show
that along with the Chang Palais-Smale condition we can obtain a global
diffeomorphism theorem.

32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
16
The categories of this paper are: stat