Asymptotic behavior of the solutions of functional-differential equation with linearly transformed argument (Q2227214)

The authors consider a generalized pantograph differential equation of neutral type \[ x'(t)=ax(t)+bx(qt)+cx'(qt) +f(t) \] where \(\mathrm{Re} \,a=0\), \(a\neq 0\), \(\{b,c\}\subset C\), \(0< q <1\). The fundamental solution of the homogeneous equation is constructed and, by the formula of variation of arbitrary constants, the formula is found for solutions of non-homogeneous equation. Asymptotic properties of sufficiently smooth solutions are derived.