Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 112, pp. 1-16.
Title: On stability and oscillation of equations with a distributed
delay which can be reduced to difference equations
Authors: Elena Braverman (Univ. of Calgary, Canada)
Sergey Zhukovskiy (Univ. of Calgary, Canada)
Abstract:
For the equation with a distributed delay
$$
x'(t) + ax(t)+ \int_0^1 x(s+[t-1])d R(s)=0
$$
we obtain necessary and sufficient conditions of stability,
exponential stability and oscillation.
These results are applied to some particular cases, such as
integro-differential equations and equations with a piecewise
constant argument. Well known results for equations with a
piecewise constant argument are obtained as special cases.
Submitted April 26, 2008. Published August 15, 2008.
Math Subject Classifications: 34K20, 34K11, 34K06, 39A11.
Key Words: Piecewise constant arguments; distributed delay;
difference equations; oscillation; stability;
exponential stability; integro-differential equations.