scholarly journals Existence, Uniqueness, and Almost Sure Exponential Stability of Solutions to Nonlinear Stochastic System with Markovian Switching and Lévy Noises

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Chao Wei
Keyword(s):  
Exponential Stability ◽  
Stochastic System ◽  
Existence And Uniqueness ◽  
Markovian Switching ◽  
Nonlinear Stochastic System ◽  
Stability Of Solutions ◽  
Uniqueness Of Solutions ◽  
Almost Sure Exponential Stability

This paper is concerned with existence, uniqueness, and almost sure exponential stability of solutions to nonlinear stochastic system with Markovian switching and Lévy noises. Firstly, the existence and uniqueness of solutions to the system is studied. Then, the almost sure exponential stability of the system is derived. Finally, an example is presented to illustrate the results.

scholarly journals Stability analysis of stochastic delay differential equations with Markovian switching driven by L${\acute{e}}$vy noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yanqiang Chang ◽  
Huabin Chen
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Markovian Switching ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Almost Surely Exponential Stability ◽  
Delay Differential

<p style='text-indent:20px;'>In this paper, the existence and uniquenesss, stability analysis for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math id="M1">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise are studied. The existence and uniqueness of such equations is simply shown by using the Picard iterative methodology. By using the generalized integral, the Lyapunov-Krasovskii function and the theory of stochastic analysis, the exponential stability in <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>th(<inline-formula><tex-math id="M3">\begin{document}$ p\geq2 $\end{document}</tex-math></inline-formula>) for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math id="M4">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise is firstly investigated. The almost surely exponential stability is also applied. Finally, an example is provided to verify our results derived.</p>

scholarly journals Stability result of the Lamé system with a delay term in the internal fractional feedback

2021 ◽  
Vol 13 (2) ◽  
pp. 336-355
Author(s):  
Abbes Benaissa ◽  
Soumia Gaouar
Keyword(s):  
Exponential Stability ◽  
Existence And Uniqueness ◽  
Semigroup Theory ◽  
Stability Result ◽  
Classical Theorem ◽  
Uniqueness Of Solutions ◽  
Delay Term ◽  
Lamé System ◽  
Lame System

Abstract In this article, we consider a Lamé system with a delay term in the internal fractional feedback. We show the existence and uniqueness of solutions by means of the semigroup theory under a certain condition between the weight of the delay term in the fractional feedback and the weight of the term without delay. Furthermore, we show the exponential stability by the classical theorem of Gearhart, Huang and Pruss.

Integral Representations for the Solution of Dynamic Bending of a Plate with Displacement-Traction Boundary Data

2003 ◽  
Vol 10 (3) ◽  
pp. 467-480
Author(s):  
Igor Chudinovich ◽  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Boundary Data ◽  
Boundary Integral Equations ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Boundary Integral ◽  
Integral Representations ◽  
Transverse Shear Deformation ◽  
Uniqueness Of Solutions ◽  
Nonstationary Boundary

Abstract The existence of distributional solutions is investigated for the time-dependent bending of a plate with transverse shear deformation under mixed boundary conditions. The problem is then reduced to nonstationary boundary integral equations and the existence and uniqueness of solutions to the latter are studied in appropriate Sobolev spaces.

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