Generalized solutions of differential equations with the derivatives of functionals in Banach spaces (Q2121947)

In the paper under review, the authors investigate the initial value problem for a differential equation with the derivatives of the functionals in Banach spaces. The solution is sought in the space of generalized functions with the support bounded on the left and its has the form of convolution of the fundamental solution of the differential operator with the right-hand side of the equation. The authors also establish some sufficient conditions for the solvability of the initial-value problem under consideration in the classes of finitely differentiable functions.