Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variation of constants formula and exponential dichotomy for non
  autonomous non densely defined Cauchy problems   In this paper we prove a variation of constants formula for a non autonomous
and non homogeneous Cauchy problems whenever the linear part is not densely
defined and is not a Hille-Yosida operator. By using this variation of
constants formula we derive a necessary and sufficient conditions for the
existence of exponential dichotomy for the evolution family generated by the
associated non autonomous homogeneous problem. We also prove a persistence
result of the exponential dichotomy for small perturbations. Finally we
illustrate our result by consider a parabolic equation with non local and non
autonomous boundary conditions.

8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph