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Existence theorems of solutions for nonlinear impulsive Volterra integral equations in Banach spaces and applications. (Chinese. English summary) Zbl 0962.45009

The authors show some existence theorems of global solutions for the nonlinear impulsive Volterra integral equations in Banach spaces by using the comparison result and the fixed-point theorem. The paper is a continuation of the articles by D. Guo [J. Appl. Math. Stochastic Anal. 6, No. 1, 35-48 (1993; Zbl 0770.45012)] and F. Chen [Appl. Math., Ser. B (Engl. Ed.) 12, No. 3, 299-306 (1997; Zbl 0913.45004)].

MSC:

45N05 Abstract integral equations, integral equations in abstract spaces
45J05 Integro-ordinary differential equations
45G10 Other nonlinear integral equations
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
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