Completeness of solutions to a differential equation with a deviating argument that is majorized by exponential functions
The authors consider the scalar equation with deviating arguments \[ Ay:=\dot y(t)+\sum_{i=1}^s a_iy(t+h_i)=f(t), \] with \(t\in B=(a,b)\), \(-\infty\leq a<b\leq\infty\), \(h_i\in \mathbb{R}\), \(h_{i+1}>h_i\), \(a_i\in \mathbb{R}\), \(i=1,2,\dots,s\). The main result is the theorem: Let be \(Ay=0\) for almost all \(t\in B\). Then \(y(t)\) belongs to the closure of the space \(\widehat M\) in \(L_2^{\text{loc}}(\overline B)\) with \(\overline B= (a+\min(h_1,0), b+\max(h_s,0))\).
differential equation with deviating arguments
scientific article; zbMATH DE number 1050649