Stochastic Semilinear Evolution Equations: Lyapunov Function, Stability, and Ultimate Boundedness

Boundedness of solutions for semilinear duffing equations

Boundedness and Exponential Stability of Highly Nonlinear Stochastic Differential Equations

In this article we consider nonlinear stochastic differential systems and use Lyapunov functions to study the boundedness and exponential asymptotic stability of solutions. We provide several examples in which we consider stochastic systems with unbounded terms.

Attraction, stability and boundedness for stochastic differential delay equations

So far there are not many results on the attractor for the solutions of stochastic differential delay equations. The main aim of this paper is to establish new results on the attractor, from which follow several new criteria on the almost surely asymptotic stability for stochastic differential delay equations. As another by product, a number of new criteria on the boundedness of the solutions a...

Boundedness for Semilinear Duffing Equations at Resonance

In this paper, we prove the boundedness of all solutions for the equation x + n 2 x + φ(x) + g (x)q(t) = 0, where n ∈ N, q(t) = q(t + 2π), φ(x) and g(x) are bounded.

Lyapunov Functionals and Stability of Stochastic Functional Differential Equations - Preamble

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