Dirichlet problem on the half-line for an abstract Euler-Poisson-Darboux equation containing powers of an unbounded operator

Abstract

We consider an abstract Euler-Poisson-Darboux equation containing powers of an unbounded operator that is the generator of a Bessel operator function. Sufficient conditions for the unique solvability of the Dirichlet problem on the half-line are obtained. The question concerning the convergence of the solution to zero at infinity is investigated