Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean-square invariant manifolds for ill-posed stochastic evolution
  equations driven by nonlinear noise   This paper discerns the invariant manifold of a class of ill-posed stochastic
evolution equations driven by a nonlinear multiplicative noise. To be more
precise, we establish the existence of mean-square random unstable invariant
manifold and only mean-square stable invariant set. Due to the lack of the
Hille-Yosida condition, we construct a modified variation of constants formula
by the resolvent operator. With the price of imposing an unusual condition
involving a non-decreasing map, we set up the Lyapunov-Perron method and derive
the required estimates. We also emphasize that the Lyapunov-Perron map in the
forward time loses the invariant due to the adaptedness, we alternatively
establish the existence of mean-square random stable sets.

8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int