Perron's theorem for linear impulsive differential equations with distributed delay

2006-08-15
Akhmet, Marat
Zafer, A.
In this paper it is shown that under a Perron condition trivial solution of linear impulsive differential equation with distributed delay is uniformly asymptotically stable.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Suggestions

Dynamic programming for a Markov-switching jump-diffusion
Azevedo, N.; Pinheiro, D.; Weber, Gerhard Wilhelm (Elsevier BV, 2014-09-01)
We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump-diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman's optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton-Jacobi-Belman equation, which turns out to be a partial in...
Monotone positive solutions for a class of second-order nonlinear differential equations
Ertem, T.; Zafer, Ağacık (Elsevier BV, 2014-03-15)
It is shown that the second-order nonlinear differential equation
Least-squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of diffusive-convective problems
Bozkaya, Canan (Elsevier BV, 2007-01-01)
Least-squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in diffusive-convective type problems with variable coefficients. The DRBEM enables us to use the fundamental solution of Laplace equation, which is easy to implement computation ally. The terms except the Laplacian are considered as the nonhomogeneity in the equation, which ar...
Hyperbolic conservation laws on manifolds. An error estimate for finite volume schemes
Lefloch, Philippe G.; Okutmuştur, Baver; Neves, Wladimir (Springer Science and Business Media LLC, 2009-07-01)
Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L (1)-error estimate for a class of finite volume schemes allowing for the approximation of entropy solutions to the initial value problem. The error in the L (1) norm is of order h (1/4) at most, where h represents the maximal diameter of elements in the family of geodesic triangulations. The proof relies on a suitable generalization of Cockburn, Coquel, and LeFloch's theo...
Forced oscillation of second-order nonlinear differential equations with positive and negative coefficients
ÖZBEKLER, ABDULLAH; Wong, J. S. W.; Zafer, Ağacık (Elsevier BV, 2011-07-01)
In this paper we give new oscillation criteria for forced super- and sub-linear differential equations by means of nonprincipal solutions.
Citation Formats
M. Akhmet and A. Zafer, “Perron’s theorem for linear impulsive differential equations with distributed delay,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 204–218, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/35735.