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Zeitschrift für Analysis und ihre Anwendungen

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Volume 14, Issue 4, 1995, pp. 899–912
DOI: 10.4171/ZAA/656

Published online: 1995-12-31

On a Generalized Integro-Differential Equation of Barbashin Type

Cheng Chur-jen[1]

(1) Tunhai University, Taichung, Taiwan

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.

Keywords: Integro-differential equations of Barbashin type, differential equations in Banach spaces, partial integral operators, Cauchy operators, boundary value problems, spectral radius, ideal spaces

Chur-jen Cheng: On a Generalized Integro-Differential Equation of Barbashin Type. Z. Anal. Anwend. 14 (1995), 899-912. doi: 10.4171/ZAA/656