Stability analysis of delay-differential equations by the method of steps and inverse Laplace transform

2009 ◽  
Vol 17 (1-2) ◽  
pp. 185-200 ◽  
Author(s):  
Tamás Kalmár-Nagy
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Laplace Transform ◽  
Delay Differential Equations ◽  
Inverse Laplace Transform ◽  
Method Of Steps ◽  
Delay Differential

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 Constructive solution of coupled second order delay differential equations with variable coefficients

1995 ◽  
Vol 18 (4) ◽  
pp. 689-700
Author(s):  
R. J. Villanueva ◽  
A. Hervas ◽  
M. V. Ferrer
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Bounded Domain ◽  
Delay Differential Equations ◽  
Approximation Error ◽  
Variable Coefficients ◽  
Second Order ◽  
Initial Value ◽  
Method Of Steps ◽  
Delay Differential

In this paper, we study initial value problems for coupld second order delay differential equations with variable coefficients. By means of the application of the method of steps and the method of Frobenius, the exact solution of the problem is constrcted. Then, in a bounded domain, a finite analytic solution with error bounds is provided. Given an admissible errorϵwe give the number of terms to be taken in the infinite series exact solution so that the approximation error be smaller than in the bounded domain.

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