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On non-absolute functional Volterra integral equations and impulsive differential equations in ordered Banach spaces. (English) Zbl 1168.45011
Summary: We derive existence and comparison results for discontinuous non-absolute functional integral equations of Volterra type in an ordered Banach space which has a regular order cone. The obtained results are then applied to first-order impulsive differential equations.
MSC:
45N05 Abstract integral equations, integral equations in abstract spaces
45G10 Other nonlinear integral equations
34A37 Ordinary differential equations with impulses
34G20 Nonlinear differential equations in abstract spaces
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
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