We study a class of integro-differential equations containing multiplication opera-tors, partial integral operators, and ordinary integral operators. Building on the usual identification of real functions of several variables and abstract functions, such integro- differential equations may be reformulated as ordinary differential equations in suitable Banach spaces. We give a representation theorem for the corresponding Cauchy operator and study the (unique) solvability of a general boundary value problem.
Cite this article
Cheng Chur-jen, On a Generalized Integro-Differential Equation of Barbashin Type. Z. Anal. Anwend. 14 (1995), no. 4, pp. 899–912