Asymptotics with respect to a parameter of solutions of linear functional-differential equations

We study the question of the number of linearly independent solutions of the equationy ⁽ⁿ⁾ (x)+(Fy) (x)+ⁿ y (x)=0,x 0, 1], in which F is a bounded linear operator acting on various normed function spaces. A number of assertions about the asymptotic behavior of these solutions with respect to , tending to infinity are established.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 11, pp. 1460–1469, November, 1990.