Representation of the local general solution of a certain class of differential-functional equations (Q916859)

The author studies the following functional differential equation in the neighbourhood of the singular critical point \(t=0\). \[ (1)\quad \dot x(at)+t^{\lambda}b(t)\dot x(t)+c(t)x(at)+d(t)x(t)=0,\quad t>0,\quad 0<\lambda <1,\quad a>1, \] where \(b(.),c(.),d(.)\in C(R^+;R)\) and b(0)\(\neq 0\). The results give the representation of a local general solution in a neighbourhood of the point \(t=0\).