On the nonhomogeneous second-order Euler operator differential equation: Explicit solutions

AbstractA variation-of-parameters method for solving the operator differential equation t2X(2) + tA1X(1) + A0X = F(t) is presented in terms of an appropriate pair of solutions of the algebraic operator equation Z2 + (A1−I)Z + A0 = 0. Under this hypothesis, existence and uniqueness conditions for two-point boundary-value problems, as well as an explicit expression for the solutions in terms of data, are given