Asymptotic behaviour of the analytic solution of the differential equation y′(t) + y(qt) = 0 as q → 1-

AbstractThe differential equation in the title has (essentially) one analytic solution y(t, q). Continuing the investigations of Feldstein and Kolb on the zeros ti (q) of the solution, first we establish the relation ti(q)=iq−i+1[1+O(1/i2)] as i → ∞, q fixed, then we determine the asymptotic distribution of the zeros and the limit ¦ v(τ/ϵ,q)¦ϵ as ϵ → + 0, where ϵ = 1 - q and τ fixed