On Solution of Nonlinear Abel]Volterra Integral Equation

This paper is devoted to studying the nonlinear Abel-Volterra integral equation of the form a x. x w t. w m x.s H dtqf x. 0-x-dF`. G a. 0 xyt.1ya with a )0 and mgR m/0,y1,y2, . . ... The uniqueness of the solution is proved and the asymptotic behavior of w x. as xª0 is obtained, provided that a x. and f x. have special power asymptotics near zero. The solution w x. in closed form is given in some cases