Boundary-value problems and Cauchy problems for the second-order Euler operator differential equation
This paper deals with some linear differential equations on an abstract space, precisely the space of bounded operators on a Hilbert space. The model equation is a second order Euler equation with operator coefficients together with several boundary value conditions. Looking for solutions of the initial value problem of the form exp (tX) an algebraic equation is derived for X. Assuming the existence of such a solution, the question of existence of solutions to the boundary value problems is expressed in terms of algebraic conditions involving X and the operator coefficients connected to the equation. Some interesting general results related to functional operator equations are employed here, with appropriate references.
space of bounded operators on a Hilbert space
second order Euler equation with operator coefficients
scientific article; zbMATH DE number 4013055
scientific article