Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays

By Jiaowan Luo. 2008

133 citations recorded by the source corpus.

The fixed-point theory is first used to consider the stability for stochastic partial differential equations with delays. Some conditions for the exponential stability in pth mean as well as in sample path of mild solutions are given. These conditions do not require the monotone decreasing behavior of the delays, which is necessary in [T. Caraballo, K. Liu, Exponential stability of mild solutions of stochastic partial differential equations with delays, Stoch. Anal. Appl. 17 (1999) 743–763; Ruhollan Jahanipur, Stability of stochastic delay evolution equations with monotone nonlinearity, Stoch. Anal. Appl. 21 (2003) 161–181]. Even in this special case, our results also improve the results in [T. Caraballo, K. Liu, Exponential stability of mild solutions of stochastic partial differential equations with delays, Stoch. Anal. Appl. 17 (1999) 743–763].

Subfields: Applied Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/e0bdfc26ffa9c9e421a012a3780dec45febe9492

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In Applied Mathematics

1. Yongxiang Li
2. Pengyu Chen
3. Xuping Zhang
4. Rathinasamy Sakthivel
5. Zuomao Yan
6. Hongwu Zhang
7. Nazim Idrisoglu Mahmudov
8. Aziz Khan

In Control and Systems Engineering

1. Rathinasamy Sakthivel
2. Zuomao Yan
3. Hongwu Zhang
4. Pengyu Chen
5. Yongxiang Li
6. Xuping Zhang
7. Nazim Idrisoglu Mahmudov
8. P. Revathi

In Finance

1. Zuomao Yan
2. Hongwu Zhang
3. P. Revathi
4. Rathinasamy Sakthivel
5. Nazim Idrisoglu Mahmudov
6. Aftab Khan
7. Aziz Khan
8. Yongxiang Li

Citations in the corpus

• Existence of solution for a fractional‐order Lotka‐Volterra reaction‐diffusion model with Mittag‐Leffler kernel (2019, methodology): “For this, applying the AB fractional integral operator defined in Singh et al11 on the model (6), we obtain u1(t) − u1(0) = 1 − α1 (α1) ( d1 ∂2 ∂x2 u1 + r∗ 1 u1[1 − a ∗ 11u1 + a ∗ 12u2 − a ∗ 13u3] ) (7)”
• Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays (2013, background): “(17) As mentioned in Luo [20], to prove the asymptotic stability it is enough to show that the operator Ψ has a fixed point in 𝐻.”
• ASYMPTOTIC STABILITY OF FRACTIONAL IMPULSIVE NEUTRAL STOCHASTIC PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY (2013, background): “In recent years, the qualitative dynamics such as the existence and uniqueness, stability for first-order impulsive partial stochastic differential equations have been extensively studied by many authors; for instance, Sakthivel and Luo [23, 24] studied the existence and asymptotic stability in p-th”
• Cauchy problem for stochastic non-autonomous evolution equations governed by noncompact evolution families (2021, methodology): “In 2008, Luo [27] discussed the exponential stability of mild solutions for stochastic partial differential equations by using the contraction mapping principle and stochastic integral technique.”
• Asymptotic stability of impulsive stochastic partial differential equations with infinite delays (2009, unknown): “Contents lists available at ScienceDirect Journal of Mathematical Analysis and Applications www.elsevier.com/locate/jmaa Asymptotic stability of impulsive stochastic partial differential equations with infinite delays R. Sakthivel a,∗, J. Luo b a Department of Mathematics, Sungkyunkwan University, S”