Cauchy Problem for Abstract Singular Equations Containing the Bessel Operator for Negative Values of the Parameter

Euler–Poisson–Darboux equation is considered, containing thegenerator of the Bessel operator function. Sufficient conditionsfor the unique solvability of the Cauchy problem for negativevalues of the equation parameter are obtained, in this case,instead of the initial condition on the first derivative, acondition on the derivative of a higher order is specified, theorder of which depends on the parameter of the equation. Thequestion of the unique solvability of the Cauchy problem for thefactorized Euler–Poisson–Darboux equation is investigated.Examples are given.