7 - Differential equations with Bessel operator

Abstract

In this chapter we find solution representations in the compact integral form to the Cauchy problem for a general form of the Euler–Poisson–Darboux equation with Bessel operator via generalized translation and spherical mean operators. Next we solve hyperbolic and ultrahyperbolic equations with Bessel operator in spaces of weighted distributions. Finally, we consider the second order singular elliptic equation and weighted fundamental solution of the Laplace–Bessel operator.