Approximation of Abstract Differential Equations

Karasözen, Bülent
Guidetti, David
In this work we study the approximation of solutions of abstract retarded functional differential equations (ARFDE) with unbounded delay by means of solutions of ARFDE with bounded delay. As consequence we establish some results of stability and existence of periodic solutions for the first one.
Journal of Mathematical Sciences


Unpredictable solutions of linear differential and discrete equations
Akhmet, Marat; Tleubergenova, Madina; Zhamanshin, Akylbek (2019-01-01)
The existence and uniqueness of unpredictable solutions in the dynamics of nonhomogeneous linear systems of differential and discrete equations are investigated. The hyperbolic cases are under discussion. The presence of unpredictable solutions confirms the existence of Poincare chaos. Simulations illustrating the chaos are provided.
Dynamics of numerical methods for cosymmetric ordinary differential equations
Govorukhin, VN; Tsybulin, VG; Karasözen, Bülent (2001-09-01)
The dynamics of numerical approximation of cosymmetric ordinary differential equations with a continuous family of equilibria is investigated. Nonconservative and Hamiltonian model systems in two dimensions are considered and these systems are integrated with several first-order Runge-Kutta methods. The preservation of symmetry and cosymmetry, the stability of equilibrium points, spurious solutions and transition to chaos are investigated by presenting analytical and numerical results. The overall performan...
On Stability of Linear Delay Differential Equations under Perron's Condition
Diblík, J.; Zafer, A. (Hindawi Limited, 2011)
The stability of the zero solution of a system of first-order linear functional differential equations with nonconstant delay is considered. Sufficient conditions for stability, uniform stability, asymptotic stability, and uniform asymptotic stability are established.
Unpredictable Oscillations for Hopfield-Type Neural Networks with Delayed and Advanced Arguments
Akhmet, Marat; Tleubergenova, Madina; Nugayeva, Zakhira (2021-03-01)
This is the first time that the method for the investigation of unpredictable solutions of differential equations has been extended to unpredictable oscillations of neural networks with a generalized piecewise constant argument, which is delayed and advanced. The existence and exponential stability of the unique unpredictable oscillation are proven. According to the theory, the presence of unpredictable oscillations is strong evidence for Poincare chaos. Consequently, the paper is a contribution to chaos ap...
Exact Solutions of Some Partial Differential Equations Using the Modified Differential Transform Method
Cansu Kurt, Ümmügülsüm; Ozkan, Ozan (2018-03-01)
In this paper, we present the modification of the differential transform method by using Laplace transform and Pade approximation to obtain closed form solutions of linear and nonlinear partial differential equations. Some illustrative examples are given to demonstrate the activeness of the proposed technique. The obtained results ensure that this modified method is capable of solving a large number of linear and nonlinear PDEs that have wide application in science and engineering. It solves the drawbacks i...
Citation Formats
B. Karasözen and D. Guidetti, “Approximation of Abstract Differential Equations,” Journal of Mathematical Sciences, pp. 3013–3054, 2004, Accessed: 00, 2021. [Online]. Available: