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.