On Solution of Nonlinear Abel–Volterra Integral Equation

AbstractThis paper is devoted to studying the nonlinear Abel-Volterra integral equation of the formϕm(x)=a(x)∏(α)∫x0ϕ(t)(x−t1−αdt+f(x)(0<x<d≤∞)with α>0 andm∈R (m≠0,−1,−2,…). The uniqueness of the solution is proved and the asymptotic behavior of ϕ(x) asx→0 is obtained, provided thata(x) andf(x) have special power asymptotics near zero. The solution ϕ(x) in closed form is given in some cases