Modulo Periodic Poisson Stable Solutions of Quasilinear Differential Equations

Akhmet, Marat
Zhamanshin, Akylbek
In this paper, modulo periodic Poisson stable functions have been newly introduced. Quasilinear differential equations with modulo periodic Poisson stable coefficients are under investigation. The existence and uniqueness of asymptotically stable modulo periodic Poisson stable solutions have been proved. Numerical simulations, which illustrate the theoretical results are provided.


Almost periodic solutions of the linear differential equation with piecewise constant argument
Akhmet, Marat (2009-10-01)
The paper is concerned with the existence and stability of almost periodic solutions of linear systems with piecewise constant argument where t∈R, x ∈ Rn [·] is the greatest integer function. The Wexler inequality [1]-[4] for the Cauchy's matrix is used. The results can be easily extended for the quasilinear case. A new technique of investigation of equations with piecewise argument, based on an integral representation formula, is proposed. Copyright © 2009 Watam Press.
Stability criteria for linear periodic impulsive Hamiltonian systems
Guseinov, G. Sh.; Zafer, Ağacık (2007-11-15)
In this paper we obtain stability criteria for linear periodic impulsive Hamiltonian systems. A Lyapunov type inequality is established. Our results improve also the ones previously obtained for systems without impulse effect. (c) 2007 Elsevier Inc. All rights reserved.
Nonoscillation and oscillation of second-order impulsive differential equations with periodic coefficients
ÖZBEKLER, ABDULLAH; Zafer, Ağacık (2012-03-01)
In this paper, we give a nonoscillation criterion for half-linear equations with periodic coefficients under fixed moments of impulse actions. The method is based on the existence of positive solutions of the related Riccati equation and a recently obtained comparison principle. In the special case when the equation becomes impulsive Hill equation new oscillation criteria are also obtained.
Backward stochastic differential equations and Feynman-Kac formula in the presence of jump processes
İncegül Yücetürk, Cansu; Yolcu Okur, Yeliz; Hayfavi, Azize; Department of Financial Mathematics (2013)
Backward Stochastic Differential Equations (BSDEs) appear as a new class of stochastic differential equations, with a given value at the terminal time T. The application area of the BSDEs is conceptually wide which is known only for forty years. In financial mathematics, El Karoui, Peng and Quenez have a fundamental and significant article called “Backward Stochastic Differential Equations in Finance” (1997) which is taken as a groundwork for this thesis. In this thesis we follow the following steps: Firstl...
Global exponential stability of neural networks with non-smooth and impact activations
Akhmet, Marat (2012-10-01)
In this paper, we consider a model of impulsive recurrent neural networks with piecewise constant argument. The dynamics are presented by differential equations with discontinuities such as impulses at fixed moments and piecewise constant argument of generalized type. Sufficient conditions ensuring the existence, uniqueness and global exponential stability of the equilibrium point are obtained. By employing Green's function we derive new result of existence of the periodic solution. The global exponential s...
Citation Formats
M. Akhmet and A. Zhamanshin, “Modulo Periodic Poisson Stable Solutions of Quasilinear Differential Equations,” ENTROPY, vol. 23, no. 11, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: