ON SOLVABILITY OF INITIAL AND BOUNDARY VALUE PROBLEMS FOR ABSTRACT FUNCTIONAL-DIFFERENTIAL EULER–POISSON–DARBOUX EQUATIONS

Abstract

In the Banach space for functional-differential equation, generalizing the Euler–Poisson–Darboux equation, the Cauchy problem and boundary value problems of Dirichlet and Neumann are consider. A sufficient condition for solvability is proved Cauchy problem and an explicit form of the resolving operator is indicated, which is written using the ones introduced by the author Bessel and Struve operator functions. For boundary value problems in the hyperbolic case, sufficient conditions for their unique solvability imposed on the operator coefficient of the equation and boundary elements.