Almost periodic solutions of retarded SICNNs with functional response on piecewise constant argument

We consider a new model for shunting inhibitory cellular neural networks, retarded functional differential equations with piecewise constant argument. The existence and exponential stability of almost periodic solutions are investigated. An illustrative example is provided.Comment: 24 pages, 1 figur

Impulsive stabilization of high-order nonlinear retarded differential equations

summary:In this paper, impulsive stabilization of high-order nonlinear retarded differential equations is investigated by using Lyapunov functions and some analysis methods. Our results show that several non-impulsive unstable systems can be stabilized by imposition of impulsive controls. Some recent results are extended and improved. An example is given to demonstrate the effectiveness of the proposed control and stabilization methods

On the Green functions of gravitational radiation theory

Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two independent variables, by virtue of a conformal symmetry at each order in perturbation theory. The Green function for the perturbative field equations is here analyzed by studying the corresponding second-order hyperbolic operator with variable coefficients, instead of using the reduction method from the retarded flat-space Green function in four dimensions. After reduction to canonical form of this hyperbolic operator, the integral representation of the solution in terms of the Riemann function is obtained. The Riemann function solves a characteristic initial-value problem for which analytic formulae leading to the numerical solution are derived.Comment: 15 pages, plain Tex. A misprint on the right-hand side of Eqs. (3.5) and (3.6) has been amende

Auto-Oscillations in Continuous Systems with Impulsive Self-Support

The surway of impulsive-continuous autonomous systems of various types is represented, especially those of in which the impulsive self-suport (ISS) generates discontinuous auto-oscillations. The main objects are: discontinuous dynamical systems, linear oscillator with one degree of freedom and ISS, scalar functional differential equations with ISS, heat conductions and vibration of the string with energy dissipation and ISS

Auto-Oscillations in Continuous Systems with Impulsive Self-Support

The surway of impulsive-continuous autonomous systems of various types is represented, especially those of in which the impulsive self-suport (ISS) generates discontinuous auto-oscillations. The main objects are: discontinuous dynamical systems, linear oscillator with one degree of freedom and ISS, scalar functional differential equations with ISS, heat conductions and vibration of the string with energy dissipation and ISS

ON IMPULSIVE IMPLICIT RIESZ-CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS WITH RETARDATION AND ANTICIPATION IN BANACH SPACES

In this paper, we investigate the existence and Ulam stability results for a class of boundary value problems for implicit Riesz-Caputo fractional differential equations with non-instantaneous impulses involving both retarded and advanced arguments. The result are based on Monch fixed point theorem associated with the technique of measure of noncompactness. An illustrative example is given to validate our main results

An application of Green-function methods to gravitational radiation theory

Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two independent variables, by virtue of a conformal symmetry at each order in perturbation theory. The Green function for the perturbative field equations is here analyzed by studying the corresponding second-order hyperbolic operator with variable coefficients, instead of using the reduction method from the retarded flat-space Green function in four dimensions. After reduction to canonical form of this hyperbolic operator, the integral representation of the solution in terms of the Riemann function is obtained. The Riemann function solves a characteristic initial-value problem for which analytic formulae leading to the numerical solution are derived.Comment: 18 pages, Revtex4. Submitted to Lecture Notes of S.I.M., volume edited by D. Cocolicchio and S. Dragomir, with kind permission by IOP to use material in Ref. [12]. arXiv admin note: substantial text overlap with arXiv:gr-qc/010107