## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

DCDS

We first prove the existence and uniqueness of pullback and random
attractors for abstract multi-valued non-autonomous and random
dynamical systems. The standard assumption of compactness of these
systems can be replaced by the assumption of asymptotic
compactness. Then, we apply the abstract theory to handle a random
reaction-diffusion equation with memory or delay terms which can
be considered on the complete past defined by $\mathbb{R}^{-}$. In
particular, we do not assume the uniqueness of solutions of these
equations.

DCDS

We consider the exponential stability of semilinear stochastic
evolution equations with delays when zero is not a solution for
these equations. We prove the existence of a non-trivial
stationary solution exponentially stable, for which we use a
general random fixed point theorem for general cocycles. We also
construct stationary solutions with the stronger property of
attracting bounded sets uniformly, by means of the theory of
random dynamical systems and their conjugation properties.

DCDS-B

We investigate the existence, uniqueness and exponential stability of non-constant
stationary solutions of stochastic semilinear evolution equations. Our main result
shows, in particular, that noise can have a stabilization effect on deterministic
equations. Moreover, we do not require any commutative condition on the noise terms.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]