A singular initial value problem for some functional differential equations

Abstract

For the initial value problem trx′(t)=at+b1x(t)+b2x(q1t)+b3trx′(q2t)+φ(t,x(t),x(q1t),x′(t),x′(q2t)), x(0)=0, where r>1, 0<qi≤1, i∈{1,2}, we find a nonempty set of continuously differentiable solutions x:(0,ρ]→ℝ, each of which possesses nice asymptotic properties when t→+0.