On the Solvability of Nonlocal Problems for the Euler–Poisson–Darboux Functional Differential Equation

In a Banach space, two nonlocal problems are studied for a functional–differential equation that generalizes the Euler–Poisson–Darboux equation, with the Erdélyi–Kober operator appearing in additional nonlocal conditions. By reducing the problems to operator equations, conditions for their unique solvability are established; these conditions are imposed on the operator coefficient of the equation and on the nonlocal data. The solution is expressed in terms of the Bessel and Struve operator functions introduced by the author. Examples are provided.