On non-absolute functional Volterra integral equations and impulsive differential equations in ordered Banach spaces. (English) Zbl 1168.45011

Heikkilä, Seppo; Seikkala, Seppo

Electron. J. Differ. Equ. 2008, Paper No. 103, 6 p. (2008).

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

Keywords:

HL integrability; Bochner integrability; ordered Banach space; dominated convergence; monotone convergence; boundary value problem; discontinuous non-absolute functional integral equations of Volterra type; first-order impulsive differential equations